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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
Biomass (E)Lactose (E)Ethanol (E)
Biomass (S)Lactose (S)Ethanol (S)
45
40
35
30
25
20
15
10
5
00 5 10
Time (h)
Con
cent
ratio
ns (
g L–1
)
15 20 25
Figure 2 Comparison of the experimental (E) and simulated
(S) kinetics of batch whey fermentation by Kluyveromyces
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
Biomass (E)Lactose (E)Ethanol (E)
Biomass (S)Lactose (S)Ethanol (S)
90
80
70
60
50
40
30
20
10
00 5 10
Time (h)
Con
cent
ratio
ns (
g L–1
)
15 20 25
Figure 3 Comparison of the experimental (E) and simulated
(S) kinetics of batch whey fermentation by Kluyveromyces
marxianus at S0 ¼ 100 g L)1, temperature 34 �C and pH
4.5.
Ethanol production from organic wastes S. Zafar et al.600
International Journal of Food Science and Technology 2005, 40, 597–604 � 2005 Institute of Food Science and Technology Trust Fund
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).
Ethanol production from organic wastes S. Zafar et al. 601
� 2005 Institute of Food Science and Technology Trust Fund International Journal of Food Science and Technology 2005, 40, 597–604
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)
Ethanol production from organic wastes S. Zafar et al.602
International Journal of Food Science and Technology 2005, 40, 597–604 � 2005 Institute of Food Science and Technology Trust Fund
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)
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