ARTICLE

Assessment of the Impact of Salinity andIrradiance on the Combined CO2 Sequestrationand Carotenoids Production by Dunaliella salina:A Mathematical Model

O.Q.F. Araujo,1 C.N. Gobbi,1 R.M. Chaloub,2 M.A.Z. Coelho1

1Escola de Quımica, Universidade Federal do Rio de Janeiro, Av. Horacio Macedo, 2030,

Edifıcio do Centro de Tecnologia Bloco E sala/209, Cidade Universitaria,

CEP: 21941-909Rio de Janeiro, RJ, Brazil; telephone: þ55-21-25627535;

fax: þ55-21-25627637; e-mail: ofelia@eq.ufrj.br2Departamento de Bioquımica, Instituto de Quımica, Universidade Federal do Rio de Janeiro,

Rio de Janeiro, RJ, Brazil

Received 8 March 2008; revision received 11 June 2008; accepted 30 July 2008

Published online ? ? ? ? in Wiley InterScience (www.interscience.wiley.com). DOI 10

.1002/bit.22079

ABSTRACT: Current anthropogenic activities have beencausing a significant increase in the atmospheric concentra-tion of CO2 over the past 60 years. To mitigate the con-sequent global warming problem, efficient technologicalsolutions, based on economical and technical grounds,are required. In this work, microalgae are studied as impor-tant biological systems of CO2 fixation into organic com-pounds through photosynthesis. These microorganisms arepotential sources of a wide variety of interesting chemicalcompounds, which can be used for commercial purposes,reducing the cost of CO2 capture and sequestration. Speci-fically, Dunaliella salina culture was studied aiming at theimpact evaluation of operational conditions over cellulargrowth and carotenoid production associated with the CO2

sequestration on focus. The main experimental parametersinvestigated were salinity and irradiance conditions. Theexperimental results supported the development of adescriptive mathematical model of the process. Based onthe proposed model, a sensitivity analysis was carried out toinvestigate the operational conditions that maximize CO2

consumption and carotenoid production, in order to guidefurther development of technological routes for CO2 capturethrough microalgae. A preliminary cost estimation of CO2

sequestration combined to carotenoids production for a200 MW power plant is presented, based on the growthrates achieved in this study.

Biotechnol. Bioeng. 2008;9999: 1–12.

� 2008 Wiley Periodicals, Inc.

KEYWORDS: Dunaliella salina; CO2 mitigation; modeling;irradiance; carotenoids

Correspondence to: O.Q.F. Araujo

Contract grant sponsor: CNPq

Contract grant number: 504358/2004-9

� 2008 Wiley Periodicals, Inc.

BIT08-2

IntroductionQ1

Recent aggravation of global warming, due to increasedlevels of greenhouse gases (GHG) in the atmosphere, resultsin sensible environmental consequences observed aroundthe world (Tomkiewicz, 2006): about 85% of GHG arerelated to CO2 (Jean-Baptiste and Ducroux, 2003). Theaverage concentration of anthropogenic CO2 in the atmo-sphere has increased from 278 ppmv in the pre-industrialera to 358 ppmv in 1996 (Simeonova and Diaz-Bone,2004Q2). Simulation of carbon cycle predict that if CO2

emissions are maintained at the present levels, by 2,100 CO2

atmospheric concentration will reach 500 ppmv (Johnstonet al., 2003).

To restrain this expansion, Kyoto Protocol established thegoal of reducing GHG emissions in 5.2% during the periodfrom 2008 to 2012, based on 1990 data (Simeonova andDiaz-Bone, 2005). Given the fossil fuels burning is the majorcontributor to anthropogenic CO2 (�6 Gt C/year)(Johnston et al., 2003), a reduction of the level of burnedfossil fuels would contribute to limiting atmospheric CO2.However, it was predicted that, until year 2020, energydemand will still be supplied by fossil fuels (Ametistovaet al., 2002). Hence, a need is imposed for removing CO2

from stationary sources, by already existing and still to bedeveloped sequestration technologies.

The ‘‘natural’’ sequestration of CO2 by plants and also byits dissolution in the oceans account for 50% of the emis-sions, while the remaining CO2 accumulates in the atmos-phere (Ametistova et al., 2002; Johnston et al., 2003). CO2

sequestration by algae, to mitigate GHG, shows promisingperspectives due to their photosynthetic capacity andgrowth rates larger than those observed for higher plants.

Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008 1

33.R1(22079)

Furthermore, microalgae cultures can yield commercialproducts of interest, such as pharmaceutical and specialtychemicals, thus overcoming sequestration costs (Boro-witzka, 1995; Pulz and Gross, 2004; Spolaore et al., 2006).

Although the great majority of microalgae productionoccurs in open ponds, cultivation in closed reactors isincreasing in Japan and Israel, with Haematococcus sp., andin Germany, with Chlorella sp. (Spolaore et al., 2006). Atpresent, microalgae biomass market produces around5,000 tons of cell dry weight per year, being responsiblefor approximately US$ 1.25� 109 per year. Nevertheless,microalgae production requires upgrading to become morecompetitive and economically viable (Spolaore et al., 2006).

Dunaliella salina is a halophilic unicellular biflagellatemicroalga that is able to adapt to a wide range of tem-perature (from 0 to 408C), with an optimum between 20 and388C, depending on the strain studied (Borowitzka et al.,1984, 1990). Probably, D. salina is the most halotoleranteukaryotic organism known, supporting a wide range of saltconcentration, from 50 mM to over 5 M NaCl (Liu andShen, 2004). This capacity is explained by its osmoregula-tion, varying the intracellular concentration of glycerol,which may reach 50% of the cell content, according to theextra-cellular osmotic pressure. Upon osmotic transition,the synthesis or elimination of glycerol is induced withinminutes, independently of protein synthesis, both in thepresence or absence of light (Ben-Amotz and Avron, 1990;Marın et al., 1998; Sadka et al., 1989). When photosynthesisis inhibited, glycerol may be produced from the breakdownof stored amide, contributing to the resistance to theosmotic pressure. Contrarily, glycerol may be convertedback to amide or excreted into the environment, whenexternal salinity decreases (Gilmour, 1990).

D. salina also possesses the ability to synthesize andaccumulate high amounts of b-carotene (Garcıa-Gonzalezet al., 2003). Under operational conditions that do notinduce carotenogenesis, the microalga presents a greencolor, containing b-carotene values (about 0.3%) similar tothose observed in other algae and plant leaves (Ben-Amotzand Avron, 1990). On the other hand, b-carotene accum-ulation is induced under conditions that retard cell growth.Under physiological stresses such as high light intensities,high salt concentrations, high temperatures and nutrientdeficiencies (sulfate or nitrate limitation), b-caroteneaccumulation can reach up to 14% of the microalga dryweight (Garcıa-Gonzalez et al., 2003; Jahnke, 1999; Marınet al., 1998; Mendoza et al., 1999). As an example of thistrade-off, whereas the optimal salinity for growth is found tobe in the range from 18% to 22% NaCl, optimal salinity forcarotenogenesis is above 27% of NaCl (Borowitzka et al.,1984, 1990). The commercial production of D. salina as asource of b-carotene was first proposed by Massyuk (1966),and has become the third major culture of microalgae inAustralia in 1986, followed by Israel and the United States(Borowitzka, 1999). Cognis Nutrition and Health is themajor world producer of D. salina, at two sites (West andSouth Australia) with a total capacity of 800 ha, being

2 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008

considered the world’s largest ‘‘farm’’ of microalgae.Products from this microalga, like biomass and b-carotene,reach prices varying from US$ 300 to 3,000 per kg (Gomezand Gonzalez, 2004; Spolaore et al., 2006).

In the present work, a quantification of the opposingeffects of different irradiance and salinity conditions onD. salina growth and carotenogenesis is addressed. There-fore, the approach was: (i) growth of D. salina underdifferent experimental conditions, such as initial cell con-centration, salinity and irradiance intensity; (ii) develop-ment of a mathematical model, adjusted to the kineticbehavior recorded experimentally. The mathematicaldescription of growth of D. salina in terms of cell responses,such as concentrations of chlorophylls and carotenoids, cellmass and CO2 consumption, employing data available froma laboratory scale, was carried out. Experiments oriented theproposal of the model structure, through sensitivity analysis,and allowed the determination of model parameter values,as well as model validation. The validated model was used todefine operational conditions that maximize CO2 con-sumption and carotenoid production.

Materials and Methods

Microorganism and Culture Conditions

D. salina is available at the Elizabeth Aidar MicroalgaeCollection of the Department of Marine Biology, FederalUniversity Fluminense (State of Rio de Janeiro, Brazil).Culture medium was prepared with seawater, according to f/2 enrichment proposed by Guillard (1975), with a salinity of1 M NaCl. After being filtered through Whatman cellulosefilter (5.0-mm nominal pore size) and Whatman GF/F1

fiberglass filter (0.7-mm nominal pore size) for removal ofsuspended material, seawater was autoclaved at 1218C for15 min. Cultures were grown in a 500 mL erlenmeyerscontaining 250 mL of f/2 medium, and maintained insuspension by magnetic stirring (about 150 rpm). Appro-priate volumes, containing starter cultures in logarithmicgrowth phase, were added to each erlenmeyer in order toyield initial densities ranging from 2.5 to 5.0� 104 cells/mL.Culture flasks were exposed to lateral illumination providedby cool-white fluorescent lamps (Sylvania daylight tubes,40 W) under a 12:12 light:dark cycle. Photosyntheticallyactive radiation (PAR) was measured at the outer flaskssurface with a LI-COR photometer (Li-Cor Inc.Q3) equipp-ed with a LI-COR 185-B quantum sensor cell.

Cell growth was followed by direct microscopy countingin culture subsamples, stained with Lugol’s acetic solution(solution of iodine in potassium iodine dissolved in aceticacid), by using the Fuchs-Rosenthal hemacytometer. Aminimum of 400 cells was considered in each analysis.Cellular biomass was determined in culture subsamples byspectrophotometric (Hach DR4000 UV) analysis, measur-ing the apparent turbidity at 750 nm, which was convertedto cell dry weight (mg/mL) through a calibration curve.

Stock culture of D. salina was maintained in f/2 mediumat 218C. Culture was exposed to light intensity of 50 mE/m2/sunder 12:12 light:dark cycle, and submitted to manualshaking once a day.

Pigment Analysis

A sample volume of 10 mL of the cultures was filteredthrough Millipore GSWPO 250 cellulose membranes(0.22-mm nominal pore size). After macerating the filtersin 8 mL 100% methanol, pigment extraction was performedat room temperature for 30 min in the dark. Then, cellulardebris were removed by centrifugation at 3,500g for 5 min at218C (Eppendorf, model 5403), and spectrophotometricanalyses were made for both chlorophylls (a and b) and totalcarotenoids according to Wellburn (1994), after subtractingthe turbidity at 750 nm, as follows:

Ca ¼ 15:65A666 � 7:34A653 (1)

Cb ¼ 27:05A653 � 11:21A666 (2)

CðxþcÞ ¼1; 000A470 � 2:86Ca � 129:2Cb

221(3)

where Al is the absorption value at specific wavelength (l),and Ca, Cb, and C(xþc) correspond to chlorophyll a,chlorophyll b, and total carotenoids (xanthophylls pluscarotenes), respectively.

Mathematical Modeling

Achieving sequestration of large amounts of CO2 requiresincreased capture, expressed in t CO2/ha/day. Photobior-eactors, in this sense, offer the possibility of higherproductivity as compared to open ponds. In order toappropriately account for the opposing effects experimen-tally evidenced, a mathematical model is of great benefit.

FOBJ ¼ wX

XNEXPI

i¼1

XNPXI

j¼1

ðXCi;j � XEXP

i;j Þ2 þ wChl

XNEXPI

i¼1

XNChlI

j¼1

ðChlCi;j � ChlEXP

i;j Þ2

þ wCar

XNEXPI

i¼1

XNCarI

j¼1

ðCarCi;j � CarEXP

i;j Þ2 þ wChl=X

XNEXPI

i¼1

XNPChlI

j¼1

ChlCi;j

XCi;j

�ChlEXP

i;j

XEXPi;j

!2

þ wCar=X

XNEXPI

i¼1

XNPCARI

j¼1

CarCi;j

XCi;j

�CarEXP

i;j

XEXPi;j

!2

þ wCar=Chl

XNEXPI

i¼1

XNPCARI

j¼1

CarCi;j

ChlCi;j

�CarEXP

i;j

ChlEXPi;j

!2

(5)

An important step in photobioreactors design andoptimization is the mathematical modeling of the photo-tropic growth. Classic models, such as Monod type, arebased on cell specific growth rate. As a first step in thephotobioreactor design, this work investigated the influence

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of irradiance and salinity on culture performance. Thedeveloped mathematical model predicts cell content ofcarotenoids and chlorophylls in terms of carbon ‘‘buildingblock.’’

The major chemical pathway in photosynthesis is theconversion of CO2 and water to carbohydrates and oxygen.The reaction can be depicted by the equation:

CO2 þ H2O þ light þ chlorophyll ! CH2O þ O2 (4)

Carbohydrates, represented by the ‘‘building block’’(CH2O), are the primary organic products formed in theprocess. The ‘‘building block’’ was considered as the mainmetabolic triggering signal, and used in the model toregulate metabolic rates. Based on the structure proposed byEnes and Saraiva (1996), CH2O content in biomass wasinitially considered as Monod type kinetics.

As input variables, the present model considers thegrowth temperature (8C), the incident light intensity (mE/m2/s) and NaCl concentration (M) in the medium. Theimpact of these variables verified experimentally on processresponses in biomass, as well as in total carotenoids, isincluded in the model (Table I).

The set of experimental measurements (NP¼ 267)consisted of cell mass (X, mg/mL, with NPX measurements),chlorophylls a plus b (Chl, mg/mL, with NPChl measure-ments) and total carotenoids (Car, mg/mL, with NPCarmeasurements). The data were divided in two subsets: (i) aset of experiments used for model identification(NEXPI¼ 14, with NPXI¼ 174; NPChlI¼ 56 andNPCARI ¼ 56), and (ii) a set of NEXPV experimentsreserved for model validation (NEXPV¼ 6, with NPXV¼ 84;84; NPChlV¼ 27 and NPCARV¼ 27).

Nonlinear estimation was carried out with MATLAB 7.0(The MathWorks Inc.Q4), employing the fminsearch routinefrom the Optimization Toolbox (Nelder and Meadalgorithm), and the model equations were numericallyintegrated with ode15s. The objective function is presentedin Equation (5):

where wX, wChl, wCar, wChl/X, wCar/X, wCar/Chl correspondto weights 10, 1, 1, 0.01, 0.01, and 0.01, arbitrarily attribut-ed to the residues in cell concentration, chlorophylls(aþ b) concentration, total carotenoids concentration,chlorophylls (aþ b) to cell ratio, total carotenoids to cell

ujo et al. et al.: Impact of Salinity and Irradiance on CO2 Sequestration 3

Table I. Functional dependence of biomass and total carotenoids

responses under input variables (salinity, irradiance, and temperature).

Input variables

Proposed functional dependence

Biomass Total carotenoids

Salinity Growth: a (1–1/(1þ e�b(NaCl–4))) e�KIb1ðNaCl�4Þ2

Irradiance Growth: KX/KXþ I0 mRSIðI0=ðmI0þ I0ÞÞ

CO2 uptake: Io/KI1þ Ioþ (Io2/KI2)

Chl synthesis: KX Chl/KX Chlþ Io

Temperature 1 þ eðKT ððT�32Þ=32ÞÞ1=ð1 þ e�Kb2ðT�32Þ2Þ

Figure 1. Influence of light intensity (I0, mE/m2/s) and salinity (NaCl, M) on the

specific growth rate (m, day�1) of Dunaliella salina.

ratio and total carotenoids to chlorophylls (aþ b) ratio,respectively.

Bounds on search variables (i.e., model parameters) wereattributed through a variable transformation, according toEquation (6):

u ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip � pLB

pUB � p

r(6)

where p is a vector of model parameters, pLB and pUB aretheir respective lower and upper bound vectors, and u is thevector of transformed parameters.

Figure 2. Growth curves of Dunaliella salina under 1 M NaCl and 50 mE/m2/s and

under 3 M NaCl and 300 mE/m2/s.

Results

Growth and Pigment Production

Influence of temperature on growth of D. salina, exposed to50 mE/m2/s irradiance in the presence of 1 M NaCl, wasconsidered both at 22 and 318C. Whereas a 0.07 day�1

growth rate was found at 228C, a 0.09 day�1 growth rate wasdetermined at the higher temperature, and essentially no lagphase was observed at 318C. Thus, all the subsequentexperiments were performed under at 31 28C.

The impact of salinity and light intensity on the specificgrowth rate was evaluated in D. salina growing in thepresence of 1–3 M NaCl and exposed to irradiances rangingfrom 50 to 300 mE/m2/s (Fig. 1). Whereas the specificgrowth rate under 300 mE/m2/s, about 0.2 day�1, was notinfluenced by salinity (Fig. 1), this parameter determinedunder 50 mE/m2/s showed a salinity dependence since it wasmaximum at moderate salinity conditions and presented anextended lag phase in the presence of 3 M NaCl (not shown).No lag phase was observed in the phototrophic growth ofD. salina under extreme conditions of salinity and irradianceused in this work, and a decline in the growth rate wasobserved in both cases after an exponential growth for 5 days(Fig. 2). Increase in salinity and irradiance (from 1 to 3 MNaCl and from 50 to 300 mE/m2/s, respectively) promoted atwofold increase in the specific growth rate.

Figure 3 describes the content of total chlorophylls (aþ b)and total carotenoids in cells growing under low light andlow salinity, as well as under high light and high salinity. In

4 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008

the last case, total carotenoids to chlorophylls (aþ b) ratiowas essentially the same (1.57–1.78) during growth, but itunderwent an increase to 2.8 due to a pronounced decreasein total chlorophyll content observed on the 16th day ofculturing. However, under low light and low salinity, theratio was initially lower than 1 but it increased progressivelyduring growth, becoming higher than 1 in the stationarygrowth phase. As described in Figure 4, maximal values ofcarotenoid specific production were achieved at highsalinities and high irradiances at early stationary growthphase (9th day of culturing).

To further investigate the benefit of light intensity oncarotenoid content, a ratio expressed as pigment improve-

Figure 3. Total carotenoids and chlorophyll (aþ b) content during growth of

Dunaliella salina in the presence of 1 M NaCl and exposed to 50 mE/m2/s and in the

presence of 3 M NaCl and exposed to 300 mE/m2/s.

ment factor (PIF) was defined as:

PIF ¼car=chlða þ bÞ300mE=m2=s

car=chlða þ bÞ200mE=m2=s

(7)

where car/chl(aþ b) is the total carotenoid to totalchlorophyll ratio under 300 and 200 mE/m2/s.

Analogously, growth improvement factor (GIF) wasdefined as:

GIF ¼X300mE=m2=s

X200mE=m2=s

(8)

Figure 4. Influence of light intensity (I0, mE/m2/s) and salinity (NaCl, M) on

specific carotenoid content (mg/g cell) of Dunaliella salina at the 9th day of culture.

Ara

where X is the biomass concentration at 300 mE/m2/s, and200 mE/m2/s.

Figure 5 presents the effects of salinity on both typesof Improvement Factors calculated at distinct phases ofD. salina cultivation. It should be stressed that values ofImprovement Factors higher than one indicate a benefiteffect on both carotenogenesis and cell growth. When cellsfrom the early growth phase were considered (8th day ofgrowth), both PIF and GIF decreased from 1.9 and 1.7 tonearly 1.0, if salinity was increased from 1 to 3 M NaCl(Fig. 5a). Cells cultured for 16 days, however, showed themaximum value for PIF at high salinity, while the one forGIF was found at 1 M NaCl (Fig. 5b). Thus, a trade-off ishere presented: operational conditions that promotecarotenogenesis decrease the benefit on cell productivity.

The Proposed Model

Experimental results showed that operational conditions,including culture time, have a great impact on cell growthand pigment content of D. salina cultivation. On the other

Figure 5. Influence of salinity on both Growth and Pigment Improvement

Factors in cells of Dunaliella salina at the 8th (a) and 16th (b) day of culture.

ujo et al. et al.: Impact of Salinity and Irradiance on CO2 Sequestration 5

hand, in the context of CO2 sequestration, cultivation has tobe carried out balancing both cell yield and carotenoidproduction, the latter being considered to reduce themitigation costs of greenhouse gases.

For batch cultivation, the model is described by Equations(9) to (14). In the sequence, [X] is the biomass concen-tration (mg/mL), [Chl] stands for chlorophylls (a and b)concentration (mg/mL), [CH2O] is the intracellular ‘‘carbonblock’’ concentration (mg/mL), [Car] is the total carote-noids concentration (mg/mL) and ½SNO3 � is the nitrateconcentration (mg/L).

Mass Balance for biomass:

d½X�dt

¼ m½X� (9a)

where

m ¼ mmax

½CH2O�=½X�KCH2O;X þ ð½CH2O�=½X�Þ

� �KX

KX þ I0

� �

� KS

KS þ ½SNO3 �

� �(9b)

mmax ¼ a 1 � 1

1 þ e�bð½NaCl��4Þ

� �

�ð1 þ eðKT ððT�32Þ=32ÞÞÞ (9c)

In Equation (9b), the exponential hyperbolic dependence ofthe growth rate on irradiance was added to account for thefact that growth occurs in the photosynthetic reductioncarbon cycle (Vunjak-Novakovic et al., 2005).

Mass Balance for chlorophylls a and b:

d½Chl�dt

¼ C½CH2O�½X�

� �f SATChl=X (10a)

where

C ¼ Cmax

KChlð½CH2O�=½X�ÞKChl þ ð½CH2O�=½X�Þ

� �KIChl

KIChl þ I0

� �(10b)

f SATChl=X ¼ 1 � 1

1 þ e�32ð½Chl=X��500Þ

� �(10c)

f SAT½Chl=X� turns off the chlorophylls synthesis when [Chl/X]>500 mg/g.

Mass Balance for total carotenoids:

d½Car�dt

¼ mRS½X�f SAT½Car=X�

� mDC

KDC

KDC þ ð½CH2O�=½X�Þ

� �½Car�½X�

� �(11a)

6 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008

where

mRS ¼ mRSI

½CH2O�=½X�KRSI þ ð½CH2O�=½X�Þ

� �I0

mIo þ I0

� �

�ðe�KIb1ð½NaCl��4Þ2

Þðe�KIb2ðT�32Þ2

Þ (11b)

f SAT½Car=X� ¼ 1 � 1

1 þ e�32ð½Car=X��100Þ

� �(11c)

f SAT½Car=X� turns off the carotenes synthesis when [Car/X]>100 mg/g.In Equations (9c) and (11b), 4 M was taken asthe upper limit of NaCl concentration, beyond whichD. salina productivity diminishes. Analogously, 328Crepresents in Equations (9c)–(12c) the optimal temperaturebeyond which the cell productivity lowered.

Mass Balance of intracellular ‘‘carbon block’’—CO2

Uptake:

d½CH2O�dt

¼ QChl � m1d½X�dt

� KRII

d½Car�dt

� �f SAT½CH2O=X�

(12a)

where

Q ¼ Qmax

KCH2O;I

KCH2O;I þ ð½CH2O�=½X�Þ

� �

� I0

KI1 þ I0 þ ðI20=KI2Þ

� �Kat

Kat þ ½X�

� �(12b)

f SAT½CH2O=X� ¼ 1 � 1

1 þ e�32ð½CH2O=X��0:6Þ

� �(12c)

and f SAT½CH2O=X� accounts for the saturation of the carbon

uptake process for [CH2O/X] >0.6 g/g.The amount of light able to penetrate a culture that has a

cross-section of several centimeters is determined as muchby cell density as by the intensity of light at the surface of theculture vessel (Golden, 1994). As cell density increases morerapidly when light intensity is increased and quickly reducesthe effective light intensity penetrating the culture, anattenuation of the incident light on photosynthesis due tocell density is added in Equation (10b) as a hyperbolicfunction (Acien Fernandez et al., 1997). On the other hand,exposure of photosynthetic organisms to high irradiancescan promote photodamage of the photosynthetic apparatus(Osmond, 1994), and Equation (12b) accounts for photo-inhibition of photosynthesis at high irradiances (AcienFernandez et al., 1997). Photoperiods of 12 h were employedon the input variable I0 (the average irradiance, being zero inthe dark period).

Mass Balance for NO�3

d SNO3½ �dt

¼ �Yd½X�dt

(13)

Mass Balance for CO2

d½CO2�dt

¼ 44

30Q½Chl� (14)

In Table II, a study of the maximum values of parametricsensitivities, SMAX

i;j , was performed around a base pointcorresponding to: [CH2O]/[X]¼ 0.32; [X]¼ 0.05 mg/mL;[Chl]¼ 0.19 mg/mL; [Car]¼ 0.14 mg/mL; ½SNO3 � ¼ 54.7 mg/L, T¼ 308C; pco2 ¼ 4:5 � 10�4 atm; pH 8.5; I0¼ 50 mE/m2/sand [NaCl]¼ 1 M. The model is valid, considering: (i)Figure 6, which shows concentration of the dots along thediagonal of the logarithmic plot of predicted and experi-mental values; (ii) sensitivity analysis, Table II, shows that allparameters impact the process responses of interest, as for atleast one response of interest, sensitivity is above 0.1.

It should be stated that the experiments were conductedwith cultures previously acclimated to the experimentalcoordinates (salinity, irradiance). As a result, except for asmall sub-set of the experimental data, no significant lag-phase was presented to the regression procedure. Accordingto Duarte (1990), lagged algal growth responses areassociated to some extrinsic growth stimulus. The authorproposes that lagged responses have an ‘‘intrinsic’’component, due to biochemical reorganization needed forrapid cell division, and an ‘‘extrinsic’’ component, due tovariability in algal growth and loss rates that result in a lag

Table II. Model parameters and maximum sensitivities of process responses

j Units Values

KCH2O;X g CH2O/g cells 0.16

KX mE/m2/s 30.72

a day�1 0.97

b mol NaCl/L 2.42

KT 8C 1.29

mI0mg Chl./mg Car. 75.53

Cmax mg Chl./day 0.81

KChl g CH2O/g cells 0.36

KIChl mE/m2/s 44.44

mRSI mg Car./day (mE/m2/s)�1 50.83

KRSI g CH2O/g cells 0.11

KIb1 mol NaCl/L 0.03

KIb2 8C�1 0.02

Qmax day�1 1.59

KCH2O;I g CH2O/g cells 0.59

KI mE/m2/s 1,103.63

KI2 (mE/m2/s)2 333.96

m1 g CH2O/g cells/day 0.28

KRII g CH2O/L/g cells 0.04

Kat g cells/L 0.57

KS mg NO�3 38.21

Y mg NO�3 /g cells 84.81

mDC mg Car./day 0.89

KDC g CH2O/g cells 0.04

Culture operational conditions: [CH2O]/[X]¼ 0.32 (Spolaore et al., 2006)54.7 mg/L, T¼ 308C; pco2 ¼ 4:5 � 10�4 atm; pH 8.5; I0¼ 50 mE/m2/s and [Na

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between enhanced cell division and population growth.Although not captured by the present model, this issue isconsidered relevant at the start-up period of operation of anindustrial plant, when exogenous variables are adjusted toachieve the operational objective.

Sensitivity of Cell Responses to Operational Conditions

Figure 7 shows the predicted and experimental results ofthe process response variables. Based on the initial valuesof the model parameters (base case), the operationalconditions and the initial values of state variables, asensitivity analysis was performed according to definition inEquation (15):

Si;jðtÞ ¼ðYiðtÞ � YB

i ðtÞÞ=YBi ðtÞ

ðPi � PBi Þ=PB

i

(15)

where Si,j is the sensitivity of the response Yi(t) to adisturbance of 10% in the parameter Pj. Superscript B refersto parameter values of the base condition. Table II displaysthe optimal values for the parameters along with themaximum values, SMAX

i;j , of parametric sensitivities for eachmodel parameter:

SMAXi;j ¼ maxðSi;jðt1; . . . ; tENDÞÞ (16)

to 5% disturbances on final values.

SMAXi;j

X (i¼ 1) Chl (i¼ 2) Car (i¼ 3)

0.41Q5 0.37 �0.20

�0.03 �0.03 �0.15

�0.72 �0.70 0.36

�0.03 �0.04 0.16

0.06 0.06 0.17

�0.03 0.02 0.13

�0.11 �0.76 �0.58

�0.03 �0.15 �0.22

�0.03 �0.05 0.19

0.12 0.04 �0.62

�0.07 �0.03 0.29

�0.06 �0.05 0.34

�0.04 �0.04 0.28

�0.34 �0.14 �1.27

�0.07 �0.06 �0.20

�0.04 �0.04 0.21

�0.27 �0.09 �1.01

0.18 0.04 0.64

0.11 0.04 0.62

�0.07 �0.05 �0.28

0.34 0.28 0.12

0.12 �0.03 0.18

�0.17 �0.08 0.70

�0.12 �0.07 0.68

; [X]¼ 0.05 mg/mL; [Chl]¼ 0.19 mg/mL; [Car]¼ 0.14 mg/mL; ½SNO3 � ¼Cl]¼ 1 M.

ujo et al. et al.: Impact of Salinity and Irradiance on CO2 Sequestration 7

Figure 6. Correlation between calculated and experimental values. Circles:

biomass (mg/mL); diamonds: chlorophylls a, b (mg/mL); triangles: chlorophylls a, b

to biomass ratio (mg/g); squares: total carotenoids (mg/mL); stars: total carotenoids to

biomass ratio (mg/g). Black filled symbols correspond to the validation dataset.

Figure 7. Simulation at the base operational conditions of the sensitivity ana-

lysis: T¼ 328C, pH 8.5, 1 M NaCl, pco2¼ 4:5 � 10�4 atm and I0¼ 150 mE/m2/s, and

initial conditions: X¼ 0.05 mg/mL, Chla,b¼ 0.19 mg/mL, CH2O/X¼ 0.32 g/g and

Car¼ 0.14 mg/mL, NO�3 ¼ 54.7 mg/L. a: Biomass (X, g/L), (b) Chlorophylls a, b (Chl,

mg/L), (c) Carotenoids (Car, mg/L).

The model developed was employed for evaluatingsensitivities of process responses to the operationalconditions. The study was performed around a base pointcorresponding to stressed conditions for the cultivation:[CH2O]/[X]¼ 0.32; [X]¼ 0.05 mg/mL; [Chl]¼ 0.19 mg/mL; [Car]¼ 0.14 mg/mL; ½SNO3 � ¼ 54.7 mg/L, T¼ 308C;pco2 ¼ 4:5 � 10�4 atm; pH 8.5; I0¼ 50 mE/m2/s and[NaCl]¼ 1 M. The sensitivities were calculated accordingto Equation (15), where Si,j is the sensitivity of the responseYi(t) to a disturbance of 5% in the operational condition Uj.Superscript B refers to the base condition

Si;jðtÞ ¼ðYiðtÞ � YB

i ðtÞÞ=YBi ðtÞ

ðUiðtÞ � UBi ðtÞÞ=UB

i ðtÞ(17)

The sensitivity surfaces are displayed in Figure 8. There isclearly a conflict between the maximum of CO2 capture,which means maximizing cell growth, and increasingpigment concentration: biomass has negative sensitivityto the three operational conditions studied (Fig. 8a), whilepigment production benefits from increasing NaCl con-centration, temperature and light intensity (e.g.,Fig. 8b and c).

Preliminary Cost Estimation of CO2 Sequestration byD. salina

Considering a photobioreactor operating with an initialbiomass concentration of 4 g (d.w.)/L, about 0.84 g (d.w.)/L/day of D. salina biomass could be obtained for a specificgrowth rate of 0.19 day�1 (as achieved in the present work).Admitting a volume:area ratio of 60 L/m2, a biomass

8 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008

productivity of 50.2 g (d.w.)/m2/day would be reached.Grobbelaar (2000), calculating CO2 fixation from biomassproductivity, employed 54.5 wt% of C per mass of drybiomass. Assuming this carbon content, the D. salina culturecould be responsible for sequestration of 100.4 g CO2/m2/day, or ca. 1 t CO2/ha/day.

The calculated productivity of 50.2 g (d.w.)/m2/day issupported by previous work in the literature (Grobbelaarand Kurano, 2003; Lee, 2001; Pulz, 2001Q6). Pulz (2001) listsproductivities and foot-prints of a variety of photobior-eactors, showing for tubular design a foot-print of 7 m3/110 m2 and biomass production of 0.8–1.2 g (d.w.)/L/day,

Figure 8. Simulation to changes of 5% on salinity (NaCl, mol/L), irradiance (I0,

mE/m2/s) and temperature (T, 8C). Culture base operational conditions: T¼ 328C, pH

8.5, 2.0 M NaCl, pco2¼ 4:5 � 10�4 atm and I0 ¼ 150 mE/m2/s, and initial conditions:

X¼ 0.05 mg/mL, Chla,b/X¼ 1 mg/g, CH2O/X¼ 0.32 g/g and Car/X¼ 1 mg/g, NO�3 ¼ 54.7

mg/L. a: Sensitivity of biomass, (b) sensitivity of chlorophylls a, b to biomass ratio, (c)

sensitivity of carotenoids to biomass ratio.

that is, a productivity of circa 64 g(d.w.)/m2/day. Althoughexperimental investigation is required for effectively acces-sing process economics, it is fair to propose, based onpublished information, that well-designed photobiorectorcould achieve the calculated productivity performance.

Considering a tropical location of the microalgae plant,benefiting from high solar intensity, and an outdoorphotobioreactor designed for operating at high cell densities(Richmond, 2000Q7), a population cell density of 4 g/L wasassumed. In the present work, high cell density was chosen

Ara

to reduce process foot-print, a relevant issue for mitigatingcompetition with agriculture crops.

For calculation purposes, a 200 MW natural gascombined cycle (NGCC) plant was considered, emittingabout 370 kg CO2/MW/h (Narula et al., 2002), totaling1,776 t/day of CO2. Sequestration of 10% of the emitted CO2

would require 177 ha of cultivation area. To achieve thistarget, the results herein provided showed that growthshould be promoted. Hence, low irradiance and low salinityshould be employed. On the other hand, to increase thecontent of total carotenoids, a requirement for the economicviability of the proposed CO2 fixing process, opposingconditions should be imposed to the culture. To trade-offthe conflict between growth and carotenogenesis require-ment, multistage reactors are proposed in the literature(Ben-Amotz, 1995; Grobbelaar, 2000). In this configuration,a production stage is separated from the necessary cell stressstage: the algae are grown in the presence of sufficientnutrients, low salinity and low irradiance, resulting in highbiomass production rates. The biomass is then submitted tooperational conditions necessary for carotenogenesis.Tafreshi and Shariati (2006) reported the cultivation ofD. salina in two separate nursery and production stages,with productivities of 0.45 and 0.30 g/m2/day, respectively.With this technological approach, operational condition forcarotenogenesis promotion would allow to reach 10% ofbiomass weight as total carotenoids, while maintaining ahigh cell growth. The corresponding production ofcarotenoids would be of approximately 8.9 t/day.

Kadam (1997) studied the economic impact of differentprocess options for capturing CO2 from flue gas andconcluded, for a 500 MW power plant, CO2 should be firstcaptured from the flue gas by amine scrubbing, compressedand transported to a region with improved land availability,within 100 km of distance. The combined cost of scrubbing,compression and transportation would totalize an annualcost of US$ 40.5/t CO2. Furthermore, Kadam estimated for apond productivity of 45 g/m2/day an algae cost of about US$209.5/t. On the other hand, it has been stated that the cost ofalgae production in photobioreactors would be 10 timeshigher than in pounds (Benemann, 1997). Based on Kadam(1997) and Benemann (1997) figures, the photobioreactorcost for the base case (Case E of Tables II and IV) wasadopted as US$ 2,095/t. Therefore the proposed installationfor capturing 10% of a 200 MW NGCC power plant wouldrange around US$ 2.3 M, a cost of US$ 43.6/t CO2.

Molina Grima et al. (2003) discuss the economics ofmicroalgae production in photobioreactors and the down-stream recovery of metabolites using eicosapentaenoic acid(EPA) recovery as a representative case study. Producing430 kg of EPA required a biomass production capacity of26.2 t (d.w.)/year and this translated to 2,620 kg of crudeesterified extract, with a biomass productivity of 1.25 kg/m3/day. The authors concluded that, for EPA, 60% of the costsarise from the recovery process. The biomass contributes40% to the EPA production costs. Assuming that MolinaGrima et al. (2003) conclusions apply to carotenoid

ujo et al. et al.: Impact of Salinity and Irradiance on CO2 Sequestration 9

Table III. Sensitivity analysis of productivity to design premises.

Variables Case A Case B Case C Case D Case E Case F Notes

Cell density (g/L) 0.5 1 2 3 4 5 X0

Specific growth rate (m, h�1) 0.19 0.19 0.19 0.19 0.19 0.19 Present work

Cell content of carotenes (mass fraction) 0.1 0.1 0.1 0.1 0.1 0.1

CO2 sequestration (t) 177.6 177.6 177.6 177.6 177.6 177.6

Production g(d.w.)/L/d 0.10 0.21 0.42 0.63 0.84 1.05 X0(emt� 1), t¼ 1 day

Reactor foot-print (L/m2) 60 60 60 60 60 60 Pulz (2001)

Productivity (g(d.w.)/m2/day) 6.3 12.6 25.1 37.7 50.2 62.8 Prod.� foot-print

Sequestration (t CO2/ha/day) 0.1 0.3 0.5 0.8 1.0 1.3 0.545 g C/g X, 44/12 g CO2/g C.

Area (ha) for CO2 sequestration 1415.8 707.9 353.9 236.0 177.0 141.6 200 MW NGCC power plant emits 1,776 t CO2 day�1

Biomass production (t(d.w.)/day) 88.9 88.9 88.9 88.9 88.9 88.9

b-Carotene production (t/day) 8.9 8.9 8.9 8.9 8.9 8.9

extraction from D. salina culture, extracting this pigmentwould raise the total cost to around US$ 7.8 M for a 200 MWNGCC power plant. For 300 days of operation per year, thecost of the combined sequestration and carotenoidproduction would be of US$ 146.9/t CO2.

Production costs are very sensitive to cell populationdensity and reactor foot-print. The design premises adoptedare that the process operates at high cell density in a well-designed photobioreactor, with foot-print compatible to thereactors reviewed by Pulz (2001): 4 g (d.w.)/L and 60 L/m2.A sensitivity analysis of algal productivity is presented inTable III, confirming a strong influence of these designpremises on the area occupied by the plant, a relevant issuefor algae processes, which could compete with agriculturecrops. In Table IV, the process profitability is analyzed facingscenarios of photobioreactor costs and carotene marketprices. The profitability is maintained for a worst casescenario of photobioreactor cost being 10 times higher thanthe base case and carotenes market price reduced to 1/10 ofits base case.

For all cases presented in Table IV, the sequestration costis far inferior to the estimated revenue associated to 8.9 t/dayproduction of carotenoids and carbon sequestration credits(CDM mechanism predicted in the Kyoto Protocol). Asdisplayed in Table IV, for the base case (CASE E2) a cost/benefit ratio of 0.030 $/1,000 $ is expected. Additional

Table IV. Sensitivity of cost/benefit ratio to photobiorea

Variables

CO2 capture costs ($/t CO2)

Reactor cost ($/t (d.w. per year))

Carotene price ($/kg)

Sequestration cost ($/t co2)

Carbon credits (1,000 $)

Carotene revenue (1,000 $)

Revenue associated to sequestration ($/t CO2)

Cost/benefit ratio ($ sequestration/$1,000 revenue)

10 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2008

credits due to other important biomass constituent (e.g.,glycerol) would contribute to increase the process revenue.

Concluding Remarks

This study presents an analysis based on experimental resultsand mathematical modeling of D. salina culture responses tooperational conditions. Specifically, the influence of NaClconcentration of the culture medium (studied in the rangeof 1–3 M) irradiance (50–300 mE/m2/s) and temperature(22–328C) were evaluated. The results confirmed previouslyreported analyses such as the results of Borowitzka et al.(1990): high salinities and irradiance promoted caroteno-genesis while inhibiting cell growth. This situation, facingthe context of mitigation of greenhouse gas effect causedby CO2, poses an interesting optimization problem. In thisdirection, a mathematical model was formulated, whichcaptured the main experimental observations.

A preliminary estimate of the cost for fixing 10% of theemissions of a 200 MW NGCC plant, by D. salina culture,with a combined production of carotenoids was presented,based on cell growth rates achieved experimentally. Aninitial biomass concentration of 4 g (d.w.)/L was assumed inan installed area of 177 ha. For 300 days of operationper year, the cost of sequestration would be of US$ 146.9/

ctor cost—Case E.

Case E1 Case E2 Case E3

40.0 40.0 40.0

20950.0 2095.0 2095.0

100.0 100.0 50.0

253.1 146.9 146.9

1065.6 1065.6 1065.6

266622.2 266622.2 26662.2

5024.17 5024.2 520.42

0.053 0.030 0.946

t CO2. This cost is far inferior to the estimated revenueassociated to 8.9 t/day production of carotenoids and carboncredit.

The mathematical tool can be used for experimentaldesign of further culture evaluation, as well as forphotobioreactors design.

The authors kindly acknowledge the financial aid of CNPq through

grant 504358/2004-9, and research scholarships given by CNPq,

FAPERJ and CAPES. We also thank to Mrs. R.E. Simoni for manu-

script revision.

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Softproofing for advanced Adobe Acrobat Users - NOTES toolNOTE: ACROBAT READER FROM THE INTERNET DOES NOT CONTAIN THE NOTES TOOL USED IN THIS PROCEDURE.

Acrobat annotation tools can be very useful for indicating changes to the PDF proof of your article.By using Acrobat annotation tools, a full digital pathway can be maintained for your page proofs.

The NOTES annotation tool can be used with either Adobe Acrobat 4.0, 5.0 or 6.0. Other annotation tools are also available in Acrobat 4.0, but this instruction sheet will concentrateon how to use the NOTES tool. Acrobat Reader, the free Internet download software from Adobe,DOES NOT contain the NOTES tool. In order to softproof using the NOTES tool you must havethe full software suite Adobe Acrobat 4.0, 5.0 or 6.0 installed on your computer.

Steps for Softproofing using Adobe Acrobat NOTES tool:

1. Open the PDF page proof of your article using either Adobe Acrobat 4.0, 5.0 or 6.0. Proofyour article on-screen or print a copy for markup of changes.

2. Go to File/Preferences/Annotations (in Acrobat 4.0) or Document/Add a Comment (in Acrobat6.0 and enter your name into the “default user” or “author” field. Also, set the font size at 9 or 10point.

3. When you have decided on the corrections to your article, select the NOTES tool from theAcrobat toolbox and click in the margin next to the text to be changed.

4. Enter your corrections into the NOTES text box window. Be sure to clearly indicate where thecorrection is to be placed and what text it will effect. If necessary to avoid confusion, you canuse your TEXT SELECTION tool to copy the text to be corrected and paste it into the NOTEStext box window. At this point, you can type the corrections directly into the NOTES textbox window. DO NOT correct the text by typing directly on the PDF page.

5. Go through your entire article using the NOTES tool as described in Step 4.

6. When you have completed the corrections to your article, go to File/Export/Annotations (inAcrobat 4.0) or Document/Add a Comment (in Acrobat 6.0).

7. When closing your article PDF be sure NOT to save changes to original file.

8. To make changes to a NOTES file you have exported, simply re-open the original PDFproof file, go to File/Import/Notes and import the NOTES file you saved. Make changes and re-export NOTES file keeping the same file name.

9. When complete, attach your NOTES file to a reply e-mail message. Be sure to include yourname, the date, and the title of the journal your article will be printed in.