Batch Kinetics and Modelling of Ethanolic Fermentation of Whey

Original article

Batch kinetics and modelling of ethanolic fermentation

of whey

Salman Zafar,1 Mohammad Owais,2* Mohammed Saleemuddin2 & Sattar Husain1

1 Department of Chemical Engineering, Aligarh Muslim University, Aligarh 202 002, India

2 Interdisciplinary Biotechnology Unit, Aligarh Muslim University, Aligarh 202 002, India

(Received 1 April 2004; Accepted in revised form 10 September 2004)

Summary The fermentation of whey by Kluyveromyces marxianus strain MTCC 1288 was studied

using varying lactose concentrations at constant temperature and pH. The increase in

substrate concentration up to a certain limit was accompanied by an increase in ethanol

formation, for example, at a substrate concentration of 10 g L)1, the production of ethanol

was 0.618 g L)1 whereas at 50 g L)1 it was 3.98 g L)1. However, an increase in lactose

concentration to 100 g L)1 led to a drastic decrease in product formation and substrate

utilization. The maximum ethanol yield was obtained with an initial lactose concentration

of 50 g L)1. A method of batch kinetics was utilized to formulate a mathematical model

using substrate and product inhibition constants. The model successfully simulated the

batch kinetics observed at S0 ¼ 10 and 50 g L)1 but failed in case of S0 ¼ 100 g L)1

because of strong substrate inhibition.

Keywords Ethanol, inhibition kinetics, kinetic model, Kluyveromyces marxianus, lactose fermentation.

Introduction

Because reserves of fossil fuels are dwindling,

production of biofuel from microbial sources,

using waste by-products as substrates, has ac-

quired strategic significance in recent years. Eth-

anol has emerged as one of the most viable options

in the arena of non-conventional sources of

energy. Ethanol has many applications in the

chemical, pharmaceutical and food industries

either as a raw material, solvent or fuel. The

annual production of industrial ethanol is

approximately 4 million tons, 80% of which is

produced by fermentation. A global annual

growth rate of ethanol consumption of around

5% has been predicted to occur over the next

20 years. Ethanol can be produced from chemical

and biochemical processes. The raw material for

the biochemical process primarily utilizes agro-

industrial wastes like molasses, maize steep liquor,

whey, etc.

Whey is a major by-product of the dairy

industry and its disposal without expensive sewage

treatments represents a major source of water

pollution. Cheese whey represents an important

environmental problem because of the high vol-

umes produced (to make 1 kg of cheese, 9 kg whey

is generated) and its high organic matter content.

Degradation of whey has a biological oxygen

demand (BOD) ranging from 40 to 50 g L)1 and a

chemical oxygen demand (COD) of 60–80 g L)1

(von Stocker & Marison, 1993). Among various

constituents of whey, lactose is the main compo-

nent responsible for its high BOD and COD.

Interestingly, it is a potential substrate for a

variety of micro-organisms such as Candida

pseudotropicalis, Kluyveromyces marxianus and

K. lactis, etc. (Ruggeri, 1988; Porro et al., 1992;

Dominguez et al., 1999, 2000). Therefore, the

development of a highly productive process for

fermenting lactose is of prime importance, as

alcoholic fermentation can offer an alternative

mode for bioremediation of cheese whey. Besides

the basic sugar lactose, whey contains vitamins

and minerals, which can improve the physiological*Correspondent: Fax: +91 571 2701081;

e-mail: [email protected]

International Journal of Food Science and Technology 2005, 40, 597–604 597

doi:10.1111/j.1365-2621.2005.00957.x

� 2005 Institute of Food Science and Technology Trust Fund

activity of the yeast cells. To achieve a good

utilization of lactose from whey it is especially

important to choose a strain with suitable physio-

logical characteristics and to model the kinetics of

the process.

The effect of initial substrate concentration on

culture growth kinetics has not been studied

extensively so far. It has also been reported that

the rate of lactose fermentation is reduced by

sugar concentrations above 2% and by the accu-

mulation of more than 5% ethanol (Guimaraes,

1999). The maximum biotransformation of whey

by K. marxianus has been reported by von Stocker

& Marison (1993) to be 30–35% when using

immobilization techniques. In this research, a

detailed set of batch kinetic data on fermentation

of lactose by K. marxianus has been collected so as

to acquire a better understanding of the environ-

mental effects (the substrate availability, in partic-

ular) on final ethanol accumulation during the

fermentation process.

An important aspect of this study included the

development of a mathematical model that can

predict suitable nutrient feeding strategies for

selective ethanol production. These can then be

experimentally implemented to minimize wasteful

experimental trials for optimization of ethanol

fermentation from lactose (or whey). The objec-

tives of the present investigation were to study the

effect of initial substrate concentration on the

production of large amounts of biomass and

ethanol by fermentation and to develop a mathe-

matical model using the batch kinetic data.

Materials and methods

Chemicals

Pure lactose was supplied by LobaChemie, Mum-

bai, India. Yeast extract, malt extract, bactopep-

tone, agar, diammonium phosphate, ammonium

sulphate, magnesium sulphate were purchased

from Hi Media Chemicals, Mumbai, India. All

the chemicals were of analytical reagent grade.

Micro-organism and maintenance

For the alcoholic fermentation of whey, a strain of

the yeast K. marxianus was used. Strain MTCC

1288 was procured from the culture collection of

the Institute of Microbial Technology (MTCC),

Chandigarh, India. The yeast was maintained on

agar slants having the following composition

(g L)1): lactose, 20; bactopeptone, 10; yeast

extract, 5; agar, 20. A 24-h growth was preserved

at a temperature of 4 �C for further use.

Inoculum preparation

A loop of micro-organism from the slant was

transferred into test tubes containing 10 mL sterile

liquid medium, which had the same composition

as was used for agar slants. The test tubes were

incubated at 30 �C for 72 h. Then the 200 mL of

sterile liquid yeast medium was placed in 1000-mL

Erlenmeyer flasks and inoculated with 5% of the

inocula and the flasks were shaken on a rotary

shaker at 3000 g at 30 �C for 24 h. Subsequent

transfer into the bioreactor was done when the

biomass concentration in the inoculation flasks

was about 2.5–3.0 g L)1.

Analytical techniques

Biomass concentration was measured in terms of

dry weight. Yeast cells were harvested by centrif-

ugation at 200 · g for 10 min at 4 �C and then

washed twice with distilled water and weighed

after a 24-h period at 100 �C. Lactose was

determined by employing the dinitrosalicyclic acid

(DNS) method for reducing sugars. Ethanol was

estimated by the dichromate colorimetric method,

which is based on the complete oxidation of

ethanol by dichromate in the presence of sulphuric

acid to form acetic acid.

Fermentation

The composition of the media for alcoholic

fermentation was (in g L)1): lactose 10, 50 and

100; yeast extract, 3.0; malt extract, 1.5;

(NH4)2HPO4, 2.0; (NH4)2SO4, 2.0; MgSO4, 0.5.

Batch fermentation was in Erlenmeyer flasks in an

anaerobic shaker at initial concentrations of lac-

tose of 10, 50 and 100 g L)1. The temperature was

controlled at 34 �C and pH was maintained at 4.5

by addition of sterile 6 n NaOH periodically.

Samples were collected at an interval of 2 h. After

recording the optical density at 580 nm, the

remaining volume of the sample was centrifuged

Ethanol production from organic wastes S. Zafar et al.598

International Journal of Food Science and Technology 2005, 40, 597–604 � 2005 Institute of Food Science and Technology Trust Fund

for 15 min. The supernatant was stored at 4 �C for

lactose and ethanol estimation.

Results and discussions

Effect of initial substrate concentration on the

culture growth and product accumulation

The batch kinetics of biomass and ethanol pro-

duction from lactose was studied at different initial

substrate concentrations (S0 ¼ 10, 50 and

100 g L)1). Figure 1 shows the kinetics of batch

fermentation of whey to ethanol by K. marxianus

at S0 ¼ 10 g L)1. Within 26 h, K. marxianus could

metabolize most of the lactose to give biomass and

ethanol concentrations of 9.53 and 0.618 g L)1

respectively. Upon increasing the concentration of

lactose to 50 g L)1, ethanol yield was increased to

3.98 g L)1 at the end of fermentation while the

biomass concentration increased insignificantly to

10.34 g L)1 as shown in Fig. 2. The low increase

in biomass concentration can be attributed to the

death of yeast cells at high ethanol concentrations

(above 5%). Surprisingly, further enhancement of

initial lactose concentration to 100 g L)1, resulted

in a sharp decrease in rate of ethanol formation as

well as in biomass production as shown in Fig. 3.

The ethanol produced was less than 3.55 g L)1

and the amount of biomass produced was

8.54 g L)1, while the unconverted lactose at the

end of fermentation was about 49 g L)1. The rate

of formation of ethanol was slightly lower at S0 ¼100 g L)1 as compared with S0 ¼ 50 g L)1

although the lactose concentration was doubled.

This abnormality might be due to the strong

negative effect of high lactose concentration on the

rate of fermentation.

It is also evident from the growth kinetics at

different substrate concentrations that an S0 of

50 g L)1 is likely to give the best possible ethanol

yield in batch fermentation. An S0 lower than

50 g L)1 would result in reduced ethanol yield

because of decreased substrate availability and S0

greater than 50 g L)1 would no longer increase

ethanol production because of strong substrate

10

Biomass (E)Lactose (E)Ethanol (E)

Biomass (S)Lactose (S)Ethanol (S)

9

8

7

6

5

4

3

2

1

00 5 10

Time (h)

Con

cent

ratio

ns (

g L–1

)

15 20 25

Figure 1 Comparison of the experimental (E) and simulated

(S) kinetics of batch whey fermentation by Kluyveromyces

marxianus at S0 ¼ 10 g L)1, temperature 34 �C and pH 4.5.

50



45

40

35

30

25

20

15

10

5

00 5 10

Time (h)

Con

cent

ratio

ns (

g L–1

)

15 20 25



marxianus at S0 ¼ 50 g L)1, temperature 34 �C and pH 4.5.

Ethanol production from organic wastes S. Zafar et al. 599

� 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 597–604

inhibition coupled with severe product inhibition

of the enzymes responsible for converting lactose

to ethanol.

Model formulation

The usual approach for mathematical modelling

of bioreactors considers isothermal systems and is

based on a single growth rate with variants of

Monod kinetics. The models derived from Monod

kinetics are simple in nature and easy to formu-

late. The second approach is that of structured

models in which metabolic changes during culti-

vation are taken into account. This method results

in detailed modelling of the regulating processes

but it requires a larger number of measurements of

variables. Another possibility is that of represent-

ing the system by using structured unsegregated

cybernetic modelling, which is an intermediate

approach between structured and unstructured

models. The cybernetic modelling technique gives

an enzyme-coupled model consisting of many

estimated parameters. Longhi et al. (2004) have

suggested a novel approach of modelling strategy

that evaluates the main metabolic routes for the

variables of interest (lactose, oxygen, cell and

ethanol) and yields a multi-route, unstructured

kinetic model. The production or consumption

rates for each route are derived but based on the

experimental data.

In most cases of inhibition kinetics, the equa-

tions are Monod-like relationships derived from

theories on the inhibition of a single enzyme. The

previous investigations in the modelling of etha-

nolic fermentation of cheese whey by Kluyverom-

yces species, based on simplified Monod kinetics,

concentrated on two parameters – the substrate

limitation constant KS, and the yield coefficient

YX/S. Researchers have neglected the influence of

inhibition kinetics on cheese whey fermentation

although it is well known that substrate and

product inhibition play an important role for this

particular type of fermentation (Guimaraes,

1999).

The model proposed here takes into account

two new parameters – substrate inhibition con-

stant KI,S and product inhibition constant KI,P –

which are specific for this particular type of

fermentation. The inclusion of additional inhibi-

tion parameters in the model is based on the fact

that the rate of lactose fermentation by K.

marxianus is reduced by sugar concentrations

above 2% and by the accumulation of more than

5% ethanol in the fermentation broth as shown by

Guimaraes (1999). Therefore, we need to take into

consideration the substrate inhibition, as well as

the product inhibition, when formulating a model

of fermentation of whey to ethanol by K. marxi-

anus (Michel et al., 1987; Hill & Robinson, 1990).

The batch kinetic data of K. marxianus strain

MTCC 1288 at S0 ¼ 50 g L)1, temperature 34 �Cand pH 4.5 were utilized for the formulation of

the mathematical model. The following simplifi-

cations were made while developing the mathe-

matical model for batch fermentation of whey by

K. marxianus:

1 The pH was known and controlled at a constant

value throughout the modelling period.

2 The temperature remained constant during the

fermentation process.

3 The substrate of importance was the carbon

source (lactose) only.

100



90

80

70

60

50

40

30

20

10

00 5 10

Time (h)

Con

cent

ratio

ns (

g L–1

)

15 20 25



marxianus at S0 ¼ 100 g L)1, temperature 34 �C and pH

4.5.



4 There was no process limitation by either

nitrogen or phosphorus and growth factors

(yeast extract, malt extract, etc.) and they are in

excess in the fermentation medium.

5 The only product of importance was ethanol.

All the other intermediates and by-products

were neglected.

6 The conversion of lactose to ethanol took place

in the absence of accumulation or consumption

of any other intermediate metabolic product.

The model developed here incorporates the

effect of two inhibition constants – substrate

inhibition constant, KI,S and product inhibition

constant, KI,P. The system of differential equations

summarized below, eqns 1–6, represents a general

mathematical model capable of describing the

batch kinetics of alcoholic fermentation of whey

by K. marxianus:

l¼lmax

S

KSþS

� �1

1þS=KI;S

� �KI;P

KI;PþP

� �; ð1Þ

dX

dt¼lmax

S

KSþS

� �1

1þS=KI;S

� �KI;P

KI;PþP

� �X; ð2Þ

qS ¼ � 1

YX=S

lþmS

� �; ð3Þ

dS

dt¼ �

h 1

YX=S

lmaxS

KSþS

� �1

1þS=KI;S

� �KI;P

KI;PþP

� �X

þmSXi; ð4Þ

qP ¼YP=S

YX=S

� �l; ð5Þ

dP

dt¼YP=S

YX=S

lmaxS

KSþS

� �1

1þS=KI;S

� �KI;P

KI;PþP

� �X; ð6Þ

where S is substrate concentration (g L)1), X is

biomass concentration (g L)1), P is product con-

centration (g L)1), l denotes specific growth rate

(h)1), lmax denotes maximum specific growth rate

(h)1), qS denotes specific substrate utilization rate

(h)1), qP is specific product formation rate (h)1),

KS is substrate limitation constant (g L)1), KI,S is

substrate inhibition constant (g L)1), KI,P is prod-

uct inhibition constant (g L)1), YX/S is yield

coefficient for cells on substrate (kgX kgS)1),

YP/S denotes yield coefficient for product on

substrate (kgP kgS)1) and mS denotes mainten-

ance coefficient for cells (kgS kgX)1 h)1).

Eqn 1 describes the rate of biomass formation

featuring Monod-type substrate limitation, the

substrate inhibition model of Andrews and the

product inhibition model of Jerusalimsky

(Moser, 1989; Rehm & Reed, 1995). Eqn 3

represents the rate of substrate consumption

which describes the substrate utilized for growth

as well as for maintenance. Eqn 5 describes the

rate of ethanol formation featuring the relation-

ship proposed by Gaden and co-workers (Aiba

et al., 1968; Luong, 1985; Moser, 1989; Blanch &

Clark, 1997).

The system of differential equations comprising

eqns 2, 4 and 6 describing the batch kinetics of

whey fermentation by K. marxianus, was solved

using Runge–Kutta method of the fourth order.

Evaluation of model parameters

In order to be able to use the general mathematical

model developed in the preceding section for

computer simulation studies of the bioreactor

performance and to verify its capability to describe

the fermentation dynamics, numerical values of

model parameters used in the model equations

have to be determined. The model identification

procedure is based on minimizing the deviations

between the model predictions and the actual

experimental data. A non-linear regression tech-

nique was used for this purpose in combination

with a set of computer programs, including

MathCAD (Mathsoft Engineering and Education

Inc., Cambridge, MA, USA) and Polymath

(Cache Corporation, Austin, TX, USA).

The model equations described previously were

simulated on a computer using optimum values of

model parameters (Table 1). Figure 2 compares

the experimental and simulated batch kinetics of

ethanol fermentation at S0 ¼ 50 g L)1. The model

was further tested to simulate the experimental

kinetics at S0 ¼ 10 g L)1 using the model param-

eters for S0 ¼ 50 g L)1 (Fig. 1). The experimental

data and model simulation shown in Figs 1 and 2

demonstrated the validity of the model. The model

was unable to describe the batch kinetics at S0 ¼100 g L)1 because of strong substrate inhibition

(Fig. 3).



The degree of significance of individual para-

meters was evaluated by the method of parametric

sensitivity analysis. The absolute parametric sen-

sitivity (APS), which characterizes the direction in

which a selected parameter is acting, was calcula-

ted as follows (Goswami & Srivastava, 2000):

APS ¼ @f

@ki� Df

ki; ð7Þ

where f is the optimized function and ki is the

parameter. The APS characterizes the direction in

which the parameter under consideration is acting.

Its positive value leads to increased difference

between the model and the experimental data, and

vice versa.

For a mutual comparison of the calculated

parametric sensitivities and the indication of the

significance of individual parameters, the relative

parametric sensitivities (RPS) is expressed, defined

as follows (Goswami & Srivastava, 2000):

RPS ¼ ki@f

f@ki

�� kiDf

fDki

��: ð8Þ

YX/S was found to be the most sensitive parameter

indicating the maximum effect of the parameter on

the overall model formulation (Table 1). There-

fore, this parameter should be estimated with

extreme care and accuracy. It was necessary to

evaluate the results of model identification from

the standpoint of data analysis. The F-test was

used with a degree of significance, a ¼ 0.05, to

check the validity of the model from a statistical

point of view. The results of the F-distribution test

showed that the model is acceptable under the

given set of conditions.

Conclusions

The model was found to be capable of reflecting

all batch culture phases to a certain degree of

accuracy. The parameters of the proposed model

were found to be in agreement with values found

in the literature. This was particularly true for

parameters YX/S and KS. The estimated value of

KS was slightly higher than those predicted by

Moresi et al. (1990) and Barba et al. (2001). In

addition, the estimated value for lmax was lower

than that estimated by Moresi et al. (1990), Barba

et al. (2001) and Longhi et al. (2004). This disag-

reement might be attributed not only to a different

species of Kluyveromyces but also to either differ-

ent operating procedures or different modelling

strategies (Table 2).

It can be concluded that the kinetic model for

batch ethanolic fermentation of whey by K.

marxianus using substrate and product inhibition

constants simulates the microbial growth, sub-

strate consumption and product formation to a

good degree of accuracy. The model considers the

inhibition of fermentation by lactose as well as

ethanol, which have been largely neglected in

previous studies. These results will be very useful

in the phase of process design of cheese whey

Table 1 Model parameters and parametric sensitivity values

for batch fermentation (S0 ¼ 50 g L)1)

Model parameters Value APS RPS

KS (g L)1) 16.068 0.009 0.124

KI,S (g L)1) 16.096 0.053 0.121

KI,P (g L)1) 5.201 )0.157 0.095

lmax (h)1) 0.401 )1.773 0.215

YX/S (g g)1) 0.219 )0.877 0.409

mS (g g)1 h)1) 0.158 3.923 0.071

YP/S (g L)1) 0.127 )0.917 0.101

APS, absolute parametric sensitivity; RPS, relative parametric

sensitivity.

Table 2 Comparative account of

kinetic parameters of the proposed

model and earlier reports

Parameters

Micro-organism Referencelmax KS KI,S KI,P YX/S

0.401 16.07 16.10 5.20 0.22 K. marxianus This work

0.318 n.a n.a. n.a 0.07 K. fragilis von Stocker & Marison (1993)

0.93 1.2 n.a. n.a. n.a. K. fragilis Moresi et al. (1990)

0.43 9.1 n.a. n.a. 0.36 K. lactis Barba et al. (2001)

n.a. n.a. n.a. n.a. 0.52 K. fragilis Bernstein et al. (1977)

0.55 n.a. n.a. n.a. 0.31 K. marxianus Longhi et al. (2004)

n.a. n.a. n.a. n.a. 0.12 K. fragilis Beausejour et al. (1981)

n.a n.a n.a n.a 0.45 K. fragilis Harju et al. (1976)



utilization, where the main operating conditions

have to be established for an efficient fermentation

process. The model predictions in the computer

process simulation could be used to direct further

experimental work on bioreactor performance and

optimization in different unconventional operating

modes. The proposals for future work include

studying the influence of pH on the model

parameters, optimization of the operating condi-

tions, generalization of the model to other fer-

mentation processes and implementation of

model-based control technologies. It is clear that

an alternative experimental strategy needs to be

implemented to overcome the problems of limited

success of fermentation of lactose in whey perme-

ate directly into ethanol, as the yields and alcohol

tolerances of the organisms capable of directly

fermenting lactose are low.

Acknowledgments

The authors express their gratitude to Prof. M.

Idrees, Chairman, Department of Chemical

Engineering (AMU, Aligarh) for providing the

necessary facilities to complete this study. This

work was supported by FIST-DST programme.

Nomenclature

KI,P Product inhibition constant (g L)1)

KI,S Substrate inhibition constant (g L)1)

KS Saturation constant (g L)1)

mS Maintenance coefficient for cells on oxygen substrate

(kgS kgX)1 h)1)

P Product concentration (g L)1)

qP Specific ethanol production rate (h)1)

qS Specific substrate utilization rate (h)1)

S Substrate concentration (g L)1)

t Time (h)

X Biomass concentration (g L)1)

YP/S Yield coefficient for product on substrate (kgP kgS)1)

YX/S Yield coefficient for cells on substrate (kgX kgS)1)

l Specific growth rate of cells (h)1)

lmax Maximum specific growth rate of cells (h)1)

References

Aiba, S., Shoda, M. & Nagatani, M. (1968). Kinetics of

product inhibition in alcohol fermentation. Biotechnology

and Bioengineering, 10, 845–864.

Barba, D. Beolchini, F. Re, G.D. Giacomo, G.D. & Veglio,

F. (2001). Kinetic analysis of Kluyveromyces lactis

fermentation of whey: batch and fed-batch operations.

Process Biochemistry, 36, 531–536.

Beausejour, D. Leduy, A. & Ramalho, R.S. (1981). Batch

cultivation of Kluyveromyces fragilis in cheese

whey. Canadian Journal of Chemical Engineering, 59,

522–526.

Bernstein, S., Tzeng, C.H. & Sisson, D. (1977). The

commercial fermentation of cheese whey for the produc-

tion of protein and/or alcohol. Biotechnology and

Bioengineering Symposium, 7, 1.

Blanch, H.W. & Clark, D.S. (1997). Biochemical Engineer-

ing. Pp. 182–198. New York: Marcel Dekker Inc.

Dominguez, L., Nelson, L. & Teixiera, J.A. (1999).

Continuous ethanol fermentation of lactose by a recom-

binant flocculating S. cerevisiae cells. Biotechnology and

Bioengineering, 64, 692–697.

Dominguez, L., Nelson, L. & Teixiera, J.A. (2000). Alcohol

production from cheese whey permeate using genetically

modified flocculent yeast cells. Biotechnology and Bioen-

gineering, 72, 507–514.

Goswami, V. & Srivastava, A.K. (2000). Batch kinetics and

modelling of propionic acid fermentation. Canadian

Journal of Chemical Engineering, 78, 522–528.

Guimaraes, W.V. (1999). Fermentation of sweet whey by

ethanologenic Escherichia coli. Biotechnology and Bioen-

gineering, 40, 41–45.

Harju, M., Heikonen, M. & Kreula, M. (1976). Milchwis-

senchaft, 46, 91–94.

Hill, G.A. & Robinson, C.W. (1990). A modified Ghose

model for batch cultures of Saccharomyces cerevisiae at

high ethanol concentration. Biotechnology and Bioengi-

neering, 44, 64–80.

Longhi, L.G.S., Luvizetto, D.J., Ferriera, L.S., Rech, R.,

Ayub, M.A.Z. & Secchi, A.R. (2004). A growth kinetic

model of Kluyveromyces marxianus cultures on cheese

whey as substrate. Journal of Industrial Microbiology and

Biotechnology, 31, 35–40.

Luong, G.H.T. (1985). Kinetic of ethanol inhibition in

alcohol fermentation. Biotechnology and Bioengineering,

27, 280–285.

Michel, A., Jacob, F., Perrier, J & Poncet, S. (1987). Yeast

production from crude sweet whey. Biotechnology and


Moresi, M., Trunfio, A. & Parente, E. (1990). Kinetics of

continuous whey fermentation by Kluyveromyces fragilis.

Journal of Chemical Technology and Biotechnology, 49,

205–222.

Moser, A. (1989). Kinetics of batch fermentation. Advances

in Biochemical Engineering, 21, 244–280.

Porro, D., Martegani, E., Ranzi, B.M. & Alberghina, L.

(1992). Lactose/whey utilization and ethanol production

by transformed S. cerevisiae cells. Biotechnology and


Rehm, H.J. & Reed, G. (1995). Fundamentals of Biochemical

Engineering, Vol. 2. Pp. 48–156. New York: VGH

Publishers Inc.



Ruggeri, P. (1988). Ethanol production from lactose by

Kluyveromyces fragilis: kinetic study of an immobilized

yeast reactor. Chemical Engineering Journal, 37,

B23–B30.

von Stocker, U. & Marison, I.W. (1993). Unconventional

utilization of whey in Switzerland. In: Bioprocess

Engineering (edited by T.K. Ghose). Pp. 342–392. Oxford:

IRS Press.



Batch Kinetics and Modelling of Ethanolic Fermentation of Whey

Documents

Transcript of Batch Kinetics and Modelling of Ethanolic Fermentation of Whey