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Identification of the growth model parameters for a culture ofChlorella vulgaris in a photobioreactor

Rayen Filali

1, 2

, Sihem Tebbani

1

, Didier Dumur

1

Arsène Isambert 2, Dominique Pareau 2, Filipa Lopes 2

1SUPELEC, Control Department, F 91192 Gif sur Yvette cedex, France

(e-mail: {rayen.filali, sihem.tebbani, didier.dumur }@supelec.fr

2 Laboratoire de Génie de Procédés et Matériaux, Ecole Centrale Paris, F 92295 Chatenay-Malabry cedex,

France (e-mail: {rayen.filali, arsene.isambert, dominique.pareau, filipa.lopes}@ecp.fr).

Abstract: The microalgae biotechnology is a very promising solution for environmental applications. Inparticular, these photosynthetic microorganisms have a great capacity to fix the carbon dioxide converting

it into biomass and other secondary metabolites. Therefore the biological CO2 fixation by microalgae has

attracted much attention. The optimization of this biological process by maintaining the algal culture under

optimal growth conditions represents a major challenge. Thus microalgae growth models are needed tooptimize the carbon dioxide consumption by microalgae in engineered systems such as photobioteactors.In this paper, a procedure to identify parameters of a microalgae growth model is described. First of all,

experiments carried out in a lab-scale photobioreactor are presented. Thereafter, a description of the

selected growth model, applied to cultures of Chlorella vulgaris, which allows the effective representationof the evolution of the specific growth rate and biomass of the Chlorella vulgaris culture in a perfectly

stirred photobioreactor is described. At last, results of our model are compared to experimental data, which

confirms the accuracy of the whole procedure.

Keywords: Chlorella vulgaris, growth model, specific growth rate, biomass, photobioreactor

1. INTRODUCTION

Currently, the concept of global warming and sustainabledevelopment has become a more and more significant issue in

the worldwide politics. Indeed, increased carbon dioxide level

in the atmosphere is the main cause of the greenhouse effect.

Therefore, researches on carbon dioxide mitigation have been

increasing recently. Biological carbon dioxide fixation by

photosynthesis has attracted much attention, as an alternative

strategy, compared with physical and chemical based

approaches (De Morais and Costa, 2007; Kondili and

Kaldellis 2007; Ragauskas et al., 2006). In particular,

microalgae are able to convert efficiently carbon dioxide, as a

carbon source, into biomass. This strategy presents several

merits such as a higher growth rate and a great photosynthetic

activity compared with terrestrial plants (Borowitzka, 1999;Chisti, 2007; Li et al., 2008). The capacity of microalgae to be

more easily incorporated into engineered systems (Carvalho et

al., 2006; Lee and Lee, 2003; Suh and Lee, 2003) is also

pointed out.

The recent expansion of environmental technology has

developed the research on the biotechnology of microalgae

(Pulz et al., 2000). Indeed, several research projects are

proposed implying the bio fixation of carbon dioxide by

microalgae cultured in photobioreactors operating in optimal

growth conditions (Garcia et al., 2007; Jacob-Lopez et al.,

2008; Lee et al., 2006; Yue and Chen, 2005). The bio fixation

of carbon dioxide represents a photosynthetic processallowing the incorporation of this carbon source to cellular

compounds such as carbohydrates and lipids. These

microorganisms are characterized by their resistance to high

CO2 concentrations (Maeda et al., 1995). Another advantage

of microalgae is the possibility of controlling and maintainingthem under optimal growth conditions in photobioreactors

(Stewart and Hessami, 2005).

Many studies have been carried out in order to select tolerant

species of microalgae to high carbon dioxide concentrations

(Hanagata et al., 1992; Kodama et al., 1993; Sung et al.,

1998; Takeuchi and al., 1992; Watanabe et al., 1992). In

photobioreactors, high carbon dioxide consumption isobserved using microalgae species of Chlorella that present

an important photosynthetic potential.

In this context, the microalgal species Chlorella vulgaris is

considered as an effective organism for the bio fixation of a

high carbon dioxide concentration (Keffer and Kleinheinz,2002). Indeed, an increase in Chlorella vulgaris’s growth rate

was measured at increased carbon dioxide levels at 30°C

(Chinnasamy et al., 2009). This green unicellular microalga

has a higher photosynthetic efficiency and carbon dioxide

fixation rate than common plants (Douskova et al., 2009).

The optimization of the biological process is carried out by

maintaining culture under optimal growth conditions. To do

this, one of the required phases is the development of a

microalgae growth model. Several authors proposed models

taking into account the influence of light (Cornet et al., 1995;

Jian Li et al., 2003; Molina Grima et al., 1999; Muller-Feuga,

1999) and carbon (Nouals, 2000) on the microalgae growth.Concerning the microalgal species Chlorella, several growth

models were proposed such as Droop model (Grover, 1999)

11th International Symposium on

Computer Applications in Biotechnology

Leuven, Belgium, July 7-9, 2010

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and models taking light into account (Ogawa and Aiba, 1968;

Tamiya et al., 1953).

This paper considers a model including both effects of light

intensity accessible per cell (denoted E ) and of total inorganic

carbon available per cell (denoted cellTIC ). In the same way,

the outgoing light intensity (denoted out I ) is estimated from

biomass concentration (denoted X ) and the incident light

intensity (denoted in I ). Several batch cultures were carried

out in an instrumented photobioreactor with Chlorella

vulgaris, as the selected organism. These experiments are

used to determine and validate the growth model.

This paper is organized as follows. The two first experimental

sections describe the bioprocess and the measurements carriedout. The third section presents the selected growth model and

the related mathematical equations. The identification

procedure used to identify parameters required by the model

is developed in the fourth section. Finally, some conclusions

and perspectives are given in Section 5.

2. BIOPROCESS DESCRIPTION

2.1 Strain and culture medium

The green unicellular microalga Chlorella vulgaris AC 149

strain was cultured and maintained in the Bristol 3 N medium

with the following composition (in mg.l-1

): NaNO3, 750;

CaCl2, 2H2O, 25; MgSO4, 7H2O, 75; FeEDTA, 20; K2HPO4,75; KH2PO4, 175 and NaCl, 20, supplemented with a solution

of microelements containing (in µg.l-1

); H3BO3, 2860; MnCl2,

4H2O, 1810 ; ZnSO4, 7H2O, 220; CuSO4, 7H2O, 80; MoO3

(85%) 36 and CoSO4, 7H2O, 90. The medium was autoclaved

at 121 ºC during 20 min before use. Cultures were maintained

at 25 ºC in a 1L Erlenmeyer’s flask containing 600 mLculture, illuminated under a continuous light intensity of 70

µE m-2

s-1

and aerated with air containing 1% (v/v) CO2 under

agitation in an incubator. The maintenance of the culture was

carried out every two weeks by pricking out 300 mL of the

culture, in the exponential phase of growth, to a newErlenmeyer’s containing sterilized medium.

2.2 Photobioreactor culture conditions and measurements

Cultures of Chlorella vulgaris were developed in a bubble

column photobioreactor (fig. 1). An experimental campaign of

three cultures was carried out in this 2.5 L bioreactor with an

illuminated area of 0.1096 m² and under different values of

surface irradiance: 69, 90 and 112 µE m 2 s -1. These cultureswere developed under an optimal constant temperature of

25°C, which was maintained by a water circulation system in

dual envelopes connected to a thermostat. The reactor was

continuously supplied by a gas mixture of air containing 5 %

(v/v) CO2, with a flow rate of 2.5 V.V.H. (gas volume perliquid culture volume per hour). The agitation of the culture

was carried out by means of an air-lift system which splits and

filters the air flow entering the photobioreactor through 0.22

µm Millipore filters located at the bottom of the column. The

gas flow rate was regulated by two mass flow meters. The

photobioreactor was equipped with a pH and a dissolvedoxygen sensors. These sensors were connected to a multi-

parameters data acquisition Consort D130. An arrangement offour OSRAM white fluorescent tubes (L30W/72) and four

OSRAM pink ones (L30W/77) around the bubble column was

used as an external light source. The increase of the light

intensity was adjusted progressively by stage by means of an

electronic ballast. The carbon dioxide supply was also

introduced progressively in order to avoid any growth

limitation by an important acidification of the medium. The

culture pH was maintained at 7.4 by the addition of a defined

volume of NaOH at 0.1 N. During these cultures, several

parameters such as cellular concentration, total inorganic

carbon concentration, incident and outgoing light intensity,

pH and dissolved oxygen concentration were measured.

Samples were collected daily at regular intervals at a sampling

port at the top of the photobioreactor.

Fig. 1. Schematic representation of the photobioreactor.

The light intensity was measured using a photometer LI-COR190SA connected to the measurement box LI-250 (Eurosep

Instruments). The average light intensity was obtained from 9

measurements taken distinctly on the total reactor surface.

The cellular concentration was measured by two differentmethods: a spectrophotometric method that measures the

optical density of the microalgal sample at 683 nm; and a

granulometric method that relies on the principle of analyzing

the spot of diffraction of a beam resulting from the interaction

of a set of microalgae particles with the incident laser beam.

The number of particles is then counted using a wet disperserLIXELL (0.1 to 1750 µm) inserted in the measuring zone or a

QICPIC (2 to 1700 µm). Total inorganic carbon in the culturemedium was determined by gas phase chromatography.

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3. BIOPROCESS MODELLING

The section aims at presenting the growth model considered

to characterize Chlorella vulgaris behavior. Among all

models described in the literature, the one used in our work isbased on the model proposed by (Nouals, 2000). This model

has been preferred to structured models like Droop’s model

(Droop, 1973) as we are going to work in a continuous mode,in a next step, and the growth will be more dependant from

operating variables than from nutrients stocks inside the cells.

This model was also considered to take into account lightinfluence on the biomass growth. This model includes

dynamic equations, kinetic expression and a light transfer

model. Dynamics is based on two mass balance equations

under the assumption of a well-stirred photobioreactor. The

first one describes the evolution of the biomass concentrationwith time whereas the second equation describes the

consumption of total inorganic carbon by the biomass.

Considering only a batch mode, the biomass evolution is

given by the relation:

X dt

dX µ = (1)

where µ the specific growth rate.

The balance of the concentration of total inorganic carbon

(TIC ) in the aqueous solution is expressed as:

])[]([][

2*2

][

COCOak Y

X µ

dt

TIC d L

TIC X

−+−= (2)

where Y X/ [TIC ] is the mass conversion yield and k La is the gas-

liquid transfer coefficient of carbon dioxide.

Furthermore, the equilibrium carbon dioxide concentration,

denoted *2[ ]CO , is defined as:

[ ] H

PCOCO 2

*2 = (3)

where PCO2 is the partial pressure of carbon dioxide and H

represents the Henry’s constant for carbon dioxide in Bristol

3 N medium.

The determination of the carbon dioxide concentration in the

medium follows the relation:

[ ]

2

2112

][

.

][1

][

++++

=

H

K K

H

K TIC CO (4)

where K 1 (pK1 = 6.35 at 25°C) and K 2 (pK2 = 10.3 at 25°C)

are the equilibrium constants of the chemical equilibriums

between CO2 and HCO3− and between HCO3

− and CO32−. [ H +]

is the concentration of hydrogen ions in the culture medium

with:

pH H −+ =10][ (5)

As far as the growth kinetic is concerned, in this model, the

specific growth rate, µ, results from the interaction betweenthe saturation effects of light intensity; and the limitation and

the inhibition effects of total inorganic carbon concentration

available to the cells. Thus, the specific growth rate of

Chlorella vulgaris can be expressed as (Nouals, 2000):

)][

).(][

][).(.(max

cellCI

CI

cellCL

cell

E TIC K

K

TIC K

TIC

E K

E µ µ

+++

= (6)

where µmax, K E , K CL, and K CI are respectively the maximal

specific growth rate, the half saturation constant by lightenergy available per cell denoted by E , the limitation constant

by [TIC cell] and the inhibition constant by [TIC cell]. These are

among the model parameters to be identified.

The total inorganic carbon concentration available per cell is

given by the following relation:

[ ] X

TIC TIC cell

][= (7)

where [TIC ] and X are the total inorganic carbon and biomass

concentration per unit culture volume, respectively.

Finally, looking at the light effect, the light intensityaccessible per cell (denoted E ) is described by the light

transfer model (Krystallidis, 1994):

X V

A I I E r out in

.

)( −= (8)

where V is the volume of the liquid phase in the bioreactor , I in,

I out and Ar are respectively the incident light intensity, the

outgoing light intensity and the bioreactor illuminated area.

The outgoing light intensity cannot be measured online, and

for control purpose, it has to be determined by an analytical

expression. It is indeed estimated from the values of the

cellular concentration and the incident light intensity by thefollowing equation:

2.1C

inout X I C I = (9)

where C 1 and C 2 depend on the reactor geometry.

To summarize, in order to determine the biomass evolution

with time, the following parameters must be identified: the

coefficients C 1 and C 2 for the determination of the outgoing

light intensity, but also the coefficients appearing in the

specific growth rate µmax, K E , K CL, and K CI .

4. IDENTIFICATION PROCEDURE

AND RESULTS VALIDATION

If only the evolution of the biomass concentration with time is

considered, the identification procedure must determine the

six parameters mentioned above. This phase is performed

considering experimental data collected from three batch

cultures of Chlorella vulgaris under different incident light

intensities.

4.1 Identification of C 1 and C 2

In the paragraphs below, the outgoing light intensity was

estimated using all the measurements of biomass

concentration and incident light intensity collected during

these three cultures.

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The identification of the coefficients C 1 and C 2 was carried

out through a linear regression, since Eq. 9 can be rewritten as

following:

21 )log()log()log( C X C I

I

in

out += (10)

From the experimental data fitting of the measured outgoingand incident light intensity, coefficients C 1 and C 2 were

determined as shown in Figure 2, with a square correlation

coefficient equal to R2 = 0.955, showing the good quality of

the resulting regression.

-1 0 1 2 3 4 5-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

log (Biomass)

l o g ( C 1 ) + l o g ( B i o m a s s e ) * C 2

Model

experimental data

R2 = 0.955

Fig. 2. Identification of coefficients C 1 and C 2.

The determined coefficients C 1 and C 2 are given in table 1.

These parameters values show an inverse relationship

between the biomass concentration and the outgoing light

intensity, which is foreseeable.

Table 1. Coefficients C 1 and C 2 identified values forChlorella vulgaris at 25 ºC

Parameter Value

C 1

C 2

0.51

−0.65

Thus, using these identified values of C 1 and C 2 and from the

relation Eq. 9, the light intensity available per cell can be

calculated from the measurement of the biomass and the

incident light intensity.

4.2 Identification of the specific growth rate model

parameters

In this paragraph, experimental data of biomass and total

inorganic carbon concentration available per cell under a

specific incident light intensity are used to estimate the

specific growth rate model parameters µ max, K E , K CL and K CI .

The calculation of these parameters in Eq. 6 was performed

through a non-linear regression, using a recursive non-linearleast squares method, with data of the light intensity and of

the total inorganic carbon concentration available per cell.

The growth rate µ on the left hand-side of Eq. 6 is determined

using biomass measurements determined in batch mode.

However, Chlorella vulgaris growth can be split in two main

phases. At first, the lag phase is characterized by a high total

inorganic carbon concentration available per cell, due to a low

initial cellular concentration. Thus, during this phase the term

representing the TIC limitation in Eq. 6 is negligible. Then,the exponential phase is such that the limitation effect of total

inorganic carbon concentration available per cell is enhanced

due to a significant diminution of [TIC cell] (fig. 3).

0 50 100 150 200 2500

0.002

0.004

0.006

0.008

0.01

0.012

0.014

time (h)

C I T

c e l l

( m o l e / 1 0 9

c e l l )

Fig. 3. Time evolution of the total inorganic carbon

concentration available per cell for a culture under an incident

light intensity of 90 µE m

−2

s

−1

.Based on this, the identification of the growth rate parameters

must consider these two phenomena and can be split also into

two phases, with a double non-linear regression: on the one

hand, a regression is carried out with lag phase data, resulting

in the identification of µmax, K E and K CI . On the other hand,

the second regression is applied to data concerning the rest of

the culture time in order to estimate K CL, the limitation

constant by [TIC cell] , using the already identified parameters.

The aim of the identification algorithm is to minimize the

error between the model specific growth rate µ and the

specific growth rate calculated through Eq. 1 with

experimental biomass data. Calculated values of the specificgrowth rate model parameters for Chlorella vulgaris are listed

in Table 2.

Using these identified parameters values, the evolutions of the

measured and modeled specific growth rate with time are

compared in Figure 4. Discontinuities in the growth rate

evolution are mainly due to sparse values of measurement.

It can be seen that the specific growth rate calculated with the

identified parameters follows significantly the shape of the

curve obtained with the experimental data of a culture under

an optimal percentage of carbon dioxide and with an incident

light intensity of 90 µE m−2

s−1

.

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Table 2. Identified values of the specific growth rate model

parameters for Chlorella vulgaris at 25 ºC

Parameter Unit Value

µmax

K E

K CIK CL

h−1

µE s−1

109cell

−1

mole 109cell

−1

mole 109cell−1

0.45

1.058

0.045

0.000126

0 50 100 150 200 2500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

time (h)

M u ( h - 1 )

Model

experimental data

Fig. 4. Evolution of the modeled and experimental specific

growth rate with time under an incident light intensity of 90

µE m−2

s−1

Finally, the cellular concentration can be calculated (Eq. 1)

using the specific growth rate (Eq. 6) with the previously

identified parameters. A follow-up of the evolution of the

biomass concentration calculated by the model is compared

with the experimental data in Figure 5. It can be noticed that

the behavior of the biomass concentration calculated by themodel perfectly coincides with that obtained by the

measurements.

0 50 100 150 200 2500

20

40

60

80

100

120

140

160

180

time (h)

B i o m a s s ( 1 0 9

c e l l . l

- 1 )

Experimental data

Model

Fig.5. Evolution of the modeled and measured biomass

concentration with time under an incident light intensity of

90 µE m−2

s−1

.

4.3 Validation of the growth model

In a second step, the growth model parameters determined

previously (Table 2) were validated by comparing the

modeled biomass concentration with data for cultures

developed at an incident light intensity of 69 µ E m−2

s−1

.

The evolution of the measured and modeled cellular

concentration with time is represented in Figure 6. In general,

a good agreement between calculated and measured data is

observed.

Consequently, our model reproduces Chlorella vulgaris

growth accurately through an adequate calculation of the

specific growth rate and the cellular concentration for a rangeof cultures under different incident light intensities.

0 50 100 150 200 2500

50

100

150

time (h)

B i o m a s s ( 1 0 9

c e l l . l

- 1 )

Experimental data

Model

Fig. 6. Evolution of the modeled biomass concentration (line)

and experimental data (markers) for a microalgal culture

developed at an incident light intensity of 69 µ E m−2

s−1

.

5. CONCLUSIONS AND PERSPECTIVES

This paper presents the procedure to identify the growth

model parameters of Chlorella vulgaris culture. Afterselecting the dynamics, kinetics and light intensity

expressions, linear and non-liner regression techniques were

used to calculate parameters needed to determine the outgoing

light intensity, and to characterize the specific growth rate.

This identification procedure performed using experimental

data collected in a lab-scale batch photobioreactor enables to

build a realistic virtual simulator of the biomass evolution of

Chlorella vulgaris culture. The obtained model that takes into

account many factors such as the effect of light intensity,

limitation and inhibition of total inorganic carbon

concentration available per cell, is a useful tool to further

design of advanced control strategies.

Perspectives will consider prior to control considerations the

identification of the parameters related to the evolution of the

total inorganic carbon concentration (Eq. 2) in order to derive

a complete simulator of the growth model. In particular, this

will require identification through specific experiments of the

gas-liquid transfer coefficient of carbon dioxide, and of the

mass conversion yield.

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