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Modeling microalgal growth in an airlift-driven raceway reactor Balachandran Ketheesan, Nagamany Nirmalakhandan ⇑ Civil Engineering Department, New Mexico State University, Las Cruces, NM 88002, USA

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

" Mathematical model for algal

biomass growth in an airlift-driven raceway. " Validated model with growth data on Nannochloropsis and Scenedesmus. " Validated model with growth data from indoor and outdoor conditions. " Predicted biomass densities agreed with measured ones with r2 > 0.96.

a r t i c l e

i n f o

Article history: Received 20 November 2012 Received in revised form 12 February 2013 Accepted 14 February 2013 Available online 28 February 2013 Keywords: Algal growth model Airlift-raceway reactor Carbon dioxide transfer Simulation

a b s t r a c t In previous proof-of-concept studies, feasibility of a new airlift-raceway conﬁguration and its energetic advantage and improved CO2 utilization efﬁciency over the traditional raceways and photobioreactors have been documented. In the current study, a mathematical model for predicting biomass growth in the airlift-raceway reactor is presented, which includes supply and transfer of CO2 and the synergetic effects of light, CO2, nitrogen, and temperature. The model was calibrated and validated with data from prototype scale versions of the reactor on two test species: Nannochloropsis salina and Scenedesmus sp., cultivated under indoor and outdoor conditions. Predictions of biomass concentrations by the proposed model agreed well with the temporal trend of the experimental data, with r2 ranging from 0.96 to 0.98, p < 0.001. A sensitivity analysis of the 10 model parameters used in this study revealed that only three of them were signiﬁcant, with sensitivity coefﬁcients ranging from 0.08 to 0.13. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Microalgae has been reported to be advantageous over conventional feedstocks such as oil crops for biodiesel production due to its higher solar energy yield, higher biomass yield, competitive net energy gains, and its potential to utilize waste streams such as carbon dioxide from ﬂue gases and nutrients from wastewaters (Weyer et al., 2010). However, recent techno-economic evaluations of biodiesel production based on the traditional algal cultivation systems, such as the open raceways, indicate that they may not be energy-efﬁcient and cost-effective for biodiesel production ⇑ Corresponding author. Tel.: +1 575 646 5378; fax: +1 575 646 6049. E-mail address: [email protected] (N. Nirmalakhandan). 0960-8524/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biortech.2013.02.028

(Singh et al., 2012). This has fueled the development of engineered photobioreactors and hybrid cultivation systems capable of higher volumetric biomass productivity per unit energy input. An airlift-raceway conﬁguration has been proposed as a possible improvement to the traditional paddlewheel-driven raceway design for improved energy-efﬁciency and CO2 utilization efﬁciency. In previous proof-of-concept studies (Ketheesan and Nirmalakhandan, 2011, 2012), it was shown that the energy required for maintaining typical circulation velocities of 8– 14 cm s1 in paddlewheel-driven raceways could be reduced 40– 80% in this airlift-raceway conﬁguration. Volumetric biomass productivities (0.085 dry g L1 day1) and CO2 utilization efﬁciencies (33%) achieved in this conﬁguration were comparable to or better than those reported for paddlewheel-driven raceways. Biomass

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productivity per unit energy input in this conﬁguration was shown to be higher than those reported for engineered photobioreactors (0.60–0.69 dry g W1 day1 vs. 0.10–0.51 dry g W1 day1) (Ketheesan and Nirmalakhandan, 2011, 2012). Based on the above ﬁndings, it is hypothesized that with further optimization in terms of energy and material inputs and operating conditions, the performance of the airlift-raceway design could be enhanced further. Since process models capable of describing biomass growth in terms of the process parameters could be beneﬁcial in predicting process performance, optimizing operating conditions, identifying sensitive parameters, and in scaling up reactor systems (Geider et al., 1998), this study was undertaken to develop, calibrate, and validate a mathematical model for the airlift-raceway reactor. While the growth of outdoor cultures could be inﬂuenced by a number of parameters independently or synergistically, most outdoor raceway systems have been designed and operated to attain the upper limit of photosynthetic yields, with excess supply of CO2 and nutrients so that growth is dependent only on two uncontrollable environmental variables i.e. sun light (intensity, duration) and temperature (Goldman, 1979). Following this line of thought, several modeling studies have been reported in the literature with the intent to establish the irradiance proﬁle inside the bulk culture with respect to the bioreactor conﬁguration and to predict biomass productivity by photosynthetic mechanisms as a function of the incident irradiance and temperature (Sukenik et al., 1987, 1991; Molina Grima et al., 1994). For instance, a theoretical framework has been established by Goldman (1979) to predict the photosynthetic yield of microalgae as a function of sunlight intensity incident on the open raceway. Sukenik et al. (1987) have modeled light attenuation effects on algal productivity in a raceway and simulated daily biomass production, and reﬁned it to a deterministic model (Sukenik et al., 1991) including photoadaptation, gross photosynthesis, and respiration as a function of irradiation and temperature. Besides, several theoretical approaches (Weyer et al., 2010) have also been proposed to estimate the upper limit of algal production in response to solar energy input. While existing models provide a basis for optimizing photosynthetic yields, such models may not be applied when growth is limited by CO2 or any other major nutrient. Since carbon content of biomass is about 50% (Becker, 1994), supply of carbon to the algal cultures could possibly limit algal growth due to poor transfer of CO2 from ambient air via surface aeration; or low transfer efﬁciency of CO2-sparged systems. The traditional approach of excess supply of CO2 may not be a sustainable option since delivery of CO2 represents a major component of cultivation costs (Becker, 1994). In this context, the need for optimizing the mass input of CO2 either under light limiting or non-light limiting condition has made modeling the supply and transfer of CO2 in the airlift-raceway reactor necessary. In this work, the use of an airlift column in an open raceway for the supply and transfer of CO2 is modeled, integrating it with a model for biomass growth incorporating the synergetic effects of growth-limiting parameters such as light, CO2, nitrogen and temperature. In contrast to existing models in the literature for open raceways, the current study will provide a useful benchmark to regulate the input of CO2 in response to temporal operational variables and culture conditions. The application of this proposed model relating the CO2 supply is that, on one hand, CO2 supply can be regulated on the basis of temporal light ﬂuctuations even when the photosynthesis is solely limited by light; and, on the other hand, maximum limit of biomass yield can be attained via augmenting the supply of photosynthetic carbon towards biomass synthesis when CO2 is the primary photosynthetic-yield determinant. In order to demonstrate the CO2-dependence of microalgal growth and to rationalize the model expressions, selective culture

conditions were maintained at different CO2-to-air ratios. The proposed model was calibrated and validated using growth data of two algal species Nannochloropsis salina (N. salina), a marine algae, and Scenedesmus sp., a fresh water algae, cultivated in two prototype versions of the airlift reactor, under indoor and outdoor conditions. 2. Methods 2.1. The airlift-raceway reactor As shown in Fig. 1, the proposed airlift-raceway system consists of an open raceway integrated with an airlift conﬁguration which enables liquid circulation and CO2 transfer. Ambient air is sparged from the bottom of the riser of the airlift section, generating a hydraulic head to maintain liquid circulation in the raceway. Supplemental CO2 is bubbled at the mid-depth of the downcomer so that the downward ﬂow of the broth through the downcomer retains the rising CO2 bubbles over a prolonged period and carries them towards the riser side, improving the bubble residence time and hence the transfer of CO2 into the broth. Details of the reactor design have been reported elsewhere (Ketheesan and Nirmalakhandan, 2012). Experimental data for calibrating and validating the model were collected from two such reactors, constructed with different riser heights: Reactor 1, with a riser height of 48 cm and culture volume of 20 L; and Reactor 2, with a riser height of 72 cm and culture volume of 23 L. 2.2. Microorganisms and culture media Growth data on a marine microalgae N. salina (Eustigmatophyceae) and a fresh water microalgae Scenedesmus sp. (Chlorophyceae) were collected to calibrate and validate the model. N. salina was cultivated in modiﬁed f/2 (Arudchelvam and Nirmalakhandan, 2012) saline media with nitrate level of 1 mM NaNO3 in the laboratory studies and with 5 mM NaNO3 in the outdoor studies; Scenedesmus sp. was cultivated in fresh water Bold’s basal medium (Bischoff and Bold, 1963) with nitrate level of 3 mM NaNO3. 2.3. Reactor operation Tracer pulse injection method (Verlaan et al., 1989) was deployed to determine the liquid circulation velocity and assess mixing characteristics in the airlift-raceway reactor (see Supplementary materials). Biomass growth data were collected in indoor and outdoor tests conducted in batch mode, under sparging with ambient air

Fig. 1. Schematic of the airlift-raceway reactor.

B. Ketheesan, N. Nirmalakhandan / Bioresource Technology 136 (2013) 689–696

continuously, at a rate of 2.4 L min1. Temperature and pH were measured continuously (Mettler Toledo M300) and OD 750 was measured daily. Light levels were measured using a Quantum PAR meter (Apogee MQ-200). Correlations between OD 750 and dry density of biomass (g L1) were used to estimate the dry density of algal cultures (Ketheesan and Nirmalakhandan, 2012). Indoor studies were conducted under constant artiﬁcial illumination provided continuously with two 40 W ﬂuorescent lights (80–90 lE m2 s1). CO2 was supplied continuously via CO2 mass ﬂow controllers (Mass-Trak model 810 C) at different rates. Growth data were collected under sparging with ambient air and with supplemental CO2 injection, under the following CO2-to-air ratios: N. salina with 0.25%, 0.5%, 1%, and 2% (vol vol1) in Reactor 1; Scenedesmus sp. with 0.25%, 0.5%, 1%, and 3% (vol vol1) in Reactor 2. Outdoor tests were conducted only with N. salina, in a greenhouse under natural irradiance where, the average incident PAR on the free surface of the raceway was recorded every 30 min. Temperature inside the greenhouse was controlled at 15 °C during night and at 22 °C during day light period. Reactor 1 was run without any supplemental CO2 sparging; while Reactor 2 was run under pH-controlled supplemental CO2 sparging, with the pH set at 7.5. In the pH-controlled tests, cumulative mass ﬂow rate of CO2 was recorded by a mass ﬂow meter (Aalborg), and the partial pressure of CO2 in the liquid phase was continuously recorded by a dissolved CO2 meter (Mettler Toledo M700).

via riser/downcomer, a bubble plume was formed immediately above the spargers, although the bulk liquid phase in the main raceway was completely mixed (McGinnis and Little, 2002). The number of gas bubbles per unit area per unit time No (m2 s1) formed at the sparger can be given as

No ¼

Qg V b Að1 eÞ

N¼

No ðw þ wb Þ

a ¼ 4pr 2 N ¼ 4pr 2

ð1Þ

where KLa,air is the surface mass transfer coefﬁcient (s1), ðC La;air C 1 Þ is the CO2 concentration driving force in liquid phase, mol m3 and Vt is the total reactor volume, m3. The mass transfer coefﬁcient of CO2 through the surface of the raceway channel, KLa,air was taken as 1.24E4 s1 (Weissman et al., 1988). 3.1.2. Modeling rate of transfer of CO2 in riser and downcomer 3.1.2.1. Modeling mass transfer coefﬁcient in riser/downcomer. Since the proposed airlift-raceway reactor involves multiple modes for transferring CO2 from gaseous phase to liquid phase, the discrete bubble plume model reported by Wuest et al. (1992) and McGinnis and Little (2002) for modeling oxygen transfer in diffused-bubble system are adapted to model CO2 mass transfer coefﬁcient, KLaCO2 (s1) in riser/downcomer. The gas phase was assumed to ﬂow in a plug ﬂow manner through the riser and the downcomer. The initial bubble size distribution and the rate of bubble formation were assumed to be constant and the distribution of the bubble sizes, represented by the Sauter-mean diameter. It was assumed that when bubbles sparged

N ðw þ wb Þ

ð4Þ

where r is the radius of gas bubbles formed at the sparger (m). Incorporating mass transfer coefﬁcient of CO2, KLCO2 (m s1) at liquid side, an expression for overall mass transfer coefﬁcient, KLaCO2 (s1) in the riser/downcomer side can be derived as

3.1. Modeling CO2 transfer

M a ¼ K La;air ðC L;air C 1 ÞV t

ð3Þ

where w is the liquid velocity (m s1) and wb is the gas terminal velocity (m s1). The total surface area of the bubbles per unit plume volume, a (m2 m3) can be expressed as

K L aCO2 ¼ 4pr2

3.1.1. Modeling rate of transfer of CO2 from the atmosphere across the free surface (Ma) The transfer of CO2 from the atmosphere across the free surface, Ma, (mol s1) can be expressed as follows.

ð2Þ

where Qg is the volume ﬂow rate of gas at the sparger (m3 s1), A is the area of cross section of the riser or downcomer (m2), Vb is the volume of one gas bubble (m3) and e is the gas hold-up. The total number of bubble ﬂux per unit plume volume, N, can therefore be expressed as:

3. Model development

Dissolved CO2 in the liquid phase is modeled ﬁrst by setting up mass balance equations considering the following processes, assuming the bulk liquid phase to be well-mixed: (i) rate of transfer of CO2 from the atmosphere across the free surface, Ma (mol s1); (ii) rate of transfer of CO2 from the sparging air in the riser, Mr (mol s1); (iii) rate of transfer of CO2 from the supplemental CO2 supply in the downcomer, Ms (mol s1); and (iv) rate of consumption of CO2 by microalgae, Mc (mol s1).

691

N K LCO2 ðw þ wb Þ

ð5Þ

Here, mass transfer coefﬁcient of O2 at liquid side was adopted from Wuest et al. (1992) to estimate the mass transfer coefﬁcient of CO2, KLCO2 (m s1) using the following equation (Tamimi et al., 1994).

K LCO2 ¼ WCO2 K LO2

ð6Þ

and

Wco2 ¼

0:5 DCO2 DO2

ð7Þ

where DCO2 is the diffusivity of CO2 in water (cm2 day1) and DO2 is the diffusivity of O2 in water (cm2 day1). 3.1.2.2. Modeling rate of transfer of CO2 from the sparging air in the riser (Mr). The rate of transfer of CO2 via the riser is modeled considering an elemental mass balance and integration, with the following assumptions: the gas phase ﬂows in a plug ﬂow manner while the liquid phase is completely mixed; and the pressure of the gas phase and the molar gas ﬂow rate remain constant with depth. Thus, the elemental mass balance on CO2 in the gas phase in the riser can be expressed as

d pðeAdzÞ y ¼ M in Mout dM r dt RT

ð8Þ

where p is total pressure in the gas phase (atm), e is the gas holdup in the riser (), A is the area of riser (m2), y is the mole fraction of CO2 in the gas phase (), R is the Ideal Gas constant (atm m3 mol1 K1), T is the absolute temperature (K), Min is the molar rate of inﬂow of CO2 into the element (mol s1), Mout is the molar rate of outﬂow of CO2 from the element (mol s1), dMr is the molar rate of transfer of CO2 from the gas phase to the liquid phase within the element (mol s1). The rate of transfer of CO2 from the gas phase to the liquid phase, dMr, can be modeled following the two-ﬁlm theory as:

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dM r ¼ K L aCO2 ð1 eÞAdz½C 1 C 1

ð9Þ 1

⁄

where KLaCO2 is the mass transfer coefﬁcient of CO2 in riser (s ), C1 is the liquid phase concentration of CO2 that is in equilibrium with the gas phase (mol m3), and C1 is the liquid phase concentration of CO2 (mol m3). Combining Eqs. (8) and (9),

d pðeAdzÞ y ¼ Gy Gðy þ dyÞ K L aCO2 ð1 eÞAdz½C 1 dt RT C1

Nc l¼ Nc þ K n ð10Þ

ð11Þ

Using dimensionless form of Henry’s Constant of CO2 (H), liquid phase concentration of CO2 that is in equilibrium with the gas phase, C1⁄, can be related to the gas phase mole fraction of CO2 by

C 1 ¼

py RTH

ð12Þ

Substituting from Eq. (12) into (11) and rearranging,

dy K L aCO2 ð1 eÞA ¼ dz G C1

py RTH

py RTH K L aCO2 ð1 eÞAp in C1 þ h C 1 exp p GRTH RTH

ð14Þ

Hence, rate of transfer of CO2 from the sparging air in the riser, Mr (mol s1) can be deduced as a function of the liquid phase CO2 concentration as

py RTH K L aCO2 ð1 eÞAp in C1 þ h M r ¼ G yin C 1 exp p GRTH RTH ð15Þ A similar derivation can be used to derive an equation for the rate of transfer of CO2 from the supplemental CO2 supply in the downcomer, Ms (mol s1). Since the liquid phase is assumed to be completely mixed (see Supplementary material), the rate of change of liquid phase concentration of CO2 can be expressed as:

V

dC 1 MWCO2 ¼ Ma MWCO2 þ M r MWCO2 þ M s MWCO2 Mc dt

ð16Þ

where V is the volume of the culture (m3), Mc is the mass rate of consumption of CO2 by algal biomass (g s1) and MWCO2 is the molecular weight of CO2 (=44 g mol1). The rate of consumption of CO2 by algal biomass can be related to the rate of growth of biomass as follows:

Mc ¼

1 dX V Y dt

ð17Þ

where Y is the yield of algal biomass on CO2 (g biomass g1 CO2), and X is the biomass concentration (g m3). 3.2. Modeling biomass growth The net growth rate of algal biomass, dX/dt, can be expressed as:

"

C1

K c þ C 1 þ C 21 =K s

#"

Iave

K e þ Iave þ I2ave =K i

# ½IðTÞ

ð19Þ

where Nc is the concentration of nitrogen in the external medium (g m3), Kn is the half saturation constant for nitrogen (g m3), Kc is the half saturation constant for CO2 (mol m3), Ks is the inhibition constant for CO2 (mol m3), Iave is the average light intensity (lE m2 s1), Ke is the half saturation constant for light (lE m2 s1), and Ki is the inhibition light intensity (lE m2 s1). Previous researchers have reported that biomass decaying rate due to respiration during the night is the same as the biomass decaying rate during the day, indicating that maintenance respiration is neither stimulated nor inhibited by growth (Geider and Osborne, 1991; Quinn et al., 2011). Therefore, the proposed model also assumed that the biomass decaying rate can account for the respiration losses throughout the day and night. The model parameters included in Eq. (19) are described in Section 3.2.1 and 3.2.2.

ð13Þ

Integrating Eq. (13) with the initial condition of y = yin at z = 0, the mole fraction of CO2 in the off gases, yout, of the riser of depth h, can be expressed as:

yout ¼

ð18Þ

where kd is the biomass decaying rate and, l is the speciﬁc growth rate that can be expressed by a Michaelis–Menten type relationship modiﬁed to include limiting effects of carbon dioxide, light, temperature and nitrogen, as follows:

where G is the molar ﬂow fate of gas (mol s1). Since the bubble residence time is short, assuming pseudo steady state conditions, Eq. (10) can be simpliﬁed to yield:

dy KL aCO2 ð1 eÞA ¼ ½C 1 C 1 dz G

dX ¼ lX k d X dt

3.2.1. Modeling the effect of light Considering incident light intensity of Io (lE m2 s1), the average light intensity within the bulk culture, Iave (lE m2 s1) can be estimated as follows (Molina Grima et al., 1994):

Iave ¼

Io ð1 eðXDK a Þ Þ XDK a

ð20Þ

where D is the culture depth (m), and Ka is the light extinction coefﬁcient for biomass (m2 g1). Ka (m2 g1) can be estimated from the following empirical equation (Molina Grima et al., 1994):

K a ¼ 1:7356X p þ 0:0199

ð21Þ

where Xp is the mass fraction of total pigment in the algae, ranging between 2% and 3% of the dry algal biomass (Molina Grima et al., 1994). Scaling laboratory scale algae growth model to predict outdoor biomass productivity may be inappropriate (Quinn et al., 2011) due to the discrepancy between constant and ﬂuctuating light intensities at various magnitudes. Therefore, the proposed model includes light intensity as a function of time, incorporating the light inhibition effects. Temperature dependence of the biomass growth is expressed in terms of Arrhenius equation, I(T) as follows:

IðTÞ ¼ lmax 1:066ðT C 20Þ

ð22Þ

where lmax is the maximum speciﬁc growth rate (day1) at 20 °C, and Tc is the temperature (°C). 3.2.2. Modeling nitrogen uptake Since batch cultures are susceptible to nitrogen deﬁciency or limitation (Rodolﬁ et al., 2009), the approaches suggested by Geider et al. (1998) and Quinn et al. (2011) were followed in this study to include the effects of intercellular and extracellular nitrogen concentration and estimate the temporal proﬁles for concentration of nitrogen Nc (g m3) in the culture media. However, remineralization of nitrogen (Geider et al., 1998) and temperature-dependent nutrient uptake efﬁciencies (Packer et al., 2011) were not included in the proposed model.

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Uptake rate of nitrogen, U (g N g dw1 day1) is expressed in terms of maximum speciﬁc uptake of nitrogen, Umax (g N g dw1 day1) as follows:

U ¼ U max gint;N gext;N

ð23Þ

where

gint;N ¼ 1 gext;N ¼

qmin q

Nc Nc þ K n

ð24Þ ð25Þ

where q is the cell quota of nitrogen in the biomass (g N g dw1) at time t, and qmin is the minimum cell quota of nitrogen in the biomass when cells cease to grow (g N g dw1). The rate of cell quota of nitrogen in the biomass (q) can be expressed as:

dq ¼U dt

ð26Þ

By deploying initial values for Nc (g m3) and q (g N g dw1 day1), temporal proﬁles of Nc, q and U can be estimated (Quinn et al., 2011). In summary, the proposed model contains three coupled equations (Eqs. (15), (16), and (19)) with eight parameters relevant to the kinetics of light, CO2, and nitrogen; and two species-speciﬁc parameters that can predict the temporal biomass density. The coupled differential equations, coded using a dynamic simulation program Extend™ (Imagine That Inc.), were solved with appropriate initial concentrations of C1o, Nco and, Xo. 3.3. Sensitivity analysis Sensitivity analysis procedure was performed on each of the model parameters to determine their signiﬁcance. For each parameter, the base value established during the calibration step was changed within a range of ±10% and four simulation runs were made to generate individual temporal proﬁles of biomass concentration for that parameter, while all the other parameters were kept ﬁxed at the base value. The four biomass concentration proﬁles were compiled to form a mean proﬁle with one standard deviation spread. Average spread of each parameter was quantiﬁed in terms of a sensitivity coefﬁcient rDx1p deﬁned as follows (Bernard et al., 2001):

rDx1p ¼

1 tf

Z 0

tf

x1ðpþDpÞ x1ðpÞ dt x1p

ð27Þ

where tf is the process time, x1(p+Dp) is the change in variable x1, due to the change in the parameter value by Dp from the base value, x1p is the value of variable x1 with respect to parameter value p. 4. Results and discussion 4.1. Model calibration and validation with N. salina under indoor conditions The model was calibrated using measured growth data of N. salina, cultivated under sparging with ambient air and continuous artiﬁcial illumination. The calibration process was initiated with eight kinetic parameters and one species-speciﬁc parameter (Ka) obtained from literature reports to get the best-ﬁt biomass growth proﬁle with r2 > 0.9 (Fig. 2a). Model parameters established by this calibration process are listed in Table 1(a and b) along with comparable literature values.

o

Fig. 2. Predicted ( ) vs. experimental ( ) biomass concentrations as a function of time under laboratory conditions, at different CO2-enrichments (a–e); and overall comparison (f). Species: N. salina.

The calibrated model was then validated with the growth data of N. salina, obtained under different CO2-to-air ratios of 0.25%, 0.5%, 1%, and 2%. The model predictions agreed well with the temporal trends in all these 4 cases as shown in Fig. 2b–e. The overall correlation coefﬁcient (r2) between the experimental and the predicted biomass concentration at different CO2-to-air ratios was 0.98 (Fig. 2f). In batch tests, biomass production with N. salina at CO2-to-air ratio of 2% was lower than that observed with other CO2-to-air ratios of 0.25%, 0.5%, and 1% (data not shown here). As reported by Hsueh et al. (2009), growth of Nannochloropsis sp. can be inhibited by unutilized CO2 due to the formation of carbonic acid in the culture media. Therefore, an inhibitory CO2 constant was introduced in the present model and activated only when the cultures of N. salina sparged with CO2-to-air ratios greater than 2%. 4.2. Model validation with Scenedesmus sp. in laboratory condition The kinetic parameters established with N. salina (Table 1a) were kept the same for Scenedesmus sp. while the species-speciﬁc parameter was recalibrated using the growth proﬁle of Scenedesmus sp. obtained under sparging with ambient air. The biomass proﬁle ﬁtted during this calibration step is compared against the measured one in Fig. 3a. The model was validated using growth data of Scenedesmus sp. cultivated under CO2-to-air ratios of 0.25%, 0.5%, 1%, and 3%. The quality of ﬁt between the predicted and measured biomass densities at these four CO2-to-air ratios was good as shown in Fig. 3b–e. The overall correlation between the predicted and experimental densities was statistically signiﬁcant with r2 = 0.98, p < 0.001 (Fig. 3f). However, predictions under sparging with ambient air showed slight deviations from the experimental values, probably due to the uptake of CO2 from bicarbonate ions (Livansky, 1992)

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Table 1 Calibrated model parameters and comparable literature values. Parameter (a) Kinetic parameters Half saturation constant for CO2 Half saturation constant for light Inhibition light intensity Maximum speciﬁc growth ratea Maximum speciﬁc growth rateb Biomass decaying rate Half saturation constant for nitrogen Minimum nitrogen cell quota Maximum uptake rate of nitrogen

a

c d

Unit

Value

Comparable literature value

Kc Ke Ki

kd Kn qmin Umax

mol m3 lE m2 s1 lE m2 s1 day1 day1 day1 g m3 g N g1 g N g1d1

9.0E-4 200 2800 2.0 1.15 0.06 0.02 0.01 0.004

8.75E-3 (Hill and Lincoln, 1981) 171 (Molina Grima et al., 1996) 2500 (Molina Grima et al., 1994) 1.73 (Benson et al., 2007) 1.1 (Molina Grima et al., 1994) 0.05 (Yang, 2011) 0.014 (Geider et al., 1998) 0.01 (Quinn et al., 2011) 0.06 (Packer et al., 2011)

Ks Ka Ka

mol m3 m2 g1 m2 g1

180 0.06 0.0758

Best ﬁt value 0.0752 for Nannochloropsis Oculata (Quinn et al., 2011)

lmax lmax

(b) Species-speciﬁc parameters Inhibition constantc Extinction coefﬁcientc Extinction coefﬁcientd b

Symbol

Indoor conditions. Outdoor conditions. For N. salina. For Scenedesmus sp.

been the most common approach to identify the individual growth determinant. As evidenced by the quality of ﬁt in the present study, the proposed model can be seen to be able to describe the algal growth dynamics by incorporating the synergetic effects of dual yield determinants. 4.3. Model calibration and validation with N. salina in outdoor conditions

o

Fig. 3. Predicted ( ) vs. experimental ( ) biomass concentrations as a function of time under laboratory conditions, at different CO2-enrichments (a–e); and overall comparison (f). Species: Scenedesmus.

under carbon-limited conditions. Since CO2 tolerance of Scenedesmus sp. has been demonstrated in several studies as high with CO2-to-air ratios of 5–40%, (Westerhoff et al., 2010), inhibitory effect of CO2 was not considered in this validation process. In the previous study (Ketheesan and Nirmalakhandan, 2012), a notable increase in algal growth was observed in the tests with CO2-enrichment (0.5–3%) compared to that in the test with ambient air. However, growth of Scenedesmus sp. seemed to be less inﬂuenced by elevated CO2-to-air ratios (0.5–3%) during declining growth phase as a consequence of co-limitation by light and nitrogen (Westerhoff et al., 2010). Concerning the multiple limiting nutrient effects in algal cultivation, speciﬁc growth rate estimations or stoichiometric evaluations (Hill and Lincoln, 1981) have

The model was calibrated (Fig. 4a) against the growth data of N. salina cultivated outdoors with on-demand supply of CO2 (pH control at 7.5). During this outdoor cultivation period (September 3, 2011 to September 22, 2011), diurnal light intensity incident on the raceway was ranging between 60 and 1100 lE m2 s1. As shown in Fig. 4b and c, the calibrated model was validated using temporal growth proﬁles of N. salina cultivated under sparging with ambient air and with supplementary CO2 (pH control at 7.5). During this cultivation period (October 31, 2011 to November 22, 2011), diurnal light intensity incident on the raceway ranged between 30 and 600 lE m2 s1. The predicted biomass densities agreed well with the measured ones with r2 of 0.98 (Fig. 4d). Photoadaptation is an imperative phenomenon in outdoor algal cultivation under ﬂuctuating light intensities. In photoadaptation process, unicellular algae physiologically adjust its photosynthetic apparatus to a given light intensity, thus optimizing the photosynthetic capacity of the cell (Falkowski, 1984). Although photoadaptation can be described by ﬁrst-order kinetics (Falkowski, 1984), modeling photoadaptation is quite complicated (Sukenik et al., 1991) due to interactions by temporal variations in the light intensity and light attenuation effects, which may require additional model parameters. Also, several literature reports have indicated that the respiration losses become signiﬁcant in outdoor cultures (2–10% of biomass production) compared to continuous illumination conditions as a result of biomass losses at night and dark respiration caused by light attenuation during day time (Grobbelaar and Soeder, 1985; Sukenik et al., 1991). Therefore, the maximum speciﬁc growth rate (lmax) of N. salina under constant light intensity (2 day1) had to be adjusted as 1.15 day1 to calibrate the model for outdoor conditions. The use of the proposed model can be illustrated by the following case; on-demand supply of CO2 via pH control (Fig. 4b) did not show any signiﬁcant increase in biomass production compared to sparging with ambient air (Fig. 4c) though both reactors were operated simultaneously under identical light intensity and temperature conditions. Since light intensity was the prominent

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Fig. 5. Sensitivity of predicted biomass concentration to ±10% variations in the three most sensitive parameters: (a) Kn; (b) Ke; and (c) lmax. Species: N. salina.

4.4. Sensitivity analysis The sensitivity analysis procedure was conducted for the eight kinetic model parameters (Kc, kd, Ke, lmax, qmin, Ki, Kn, and Umax) and the two species-speciﬁc parameters (Ka and Ks) where, the impact of ±10% variation in the value of each parameter was simulated. Growth of N. salina under sparging with ambient air under indoor condition was simulated for this analysis. Based on the sensitivity coefﬁcients calculated from these simulations, maximum speciﬁc growth rate, lmax (rxDp ¼ 0:13) was found to be the most sensitized parameter followed by the half saturation constant for light, Ke (rxDp ¼ 0:11) and the half saturation constant for nitrogen, Kn (rxDp ¼ 0:08). The deviations of the simulated biomass growth proﬁles in these three cases relative to the base proﬁle are illustrated in Figs 5a–c.

0.8

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Case 1: 0.014 g/cu m Case 2: 0.028 g/cu m

0.6

80 0.4 60

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40

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growth determinant for biomass growth, supply of carbon via ambient air alone was adequate to sustain the photosynthetic carbon needs in that case, which is well accounted for by the proposed model.

Net costs [US cents/kW-hr]

o

Fig. 4. Predicted ( ) vs. experimental ( ) biomass concentrations as a function of time under ﬁeld conditions, with and without pH-control (a–c); and overall comparison (d). Species: N. salina.

CO2 utilization efﬁciency or CO2 ﬁxation rate instead (Westerhoff et al., 2010). Based on the model’s ability to predict well the growth under various CO2 enrichments, it is proposed that the model could be used to optimize the CO2 enrichment to maximize net energy production costs. As an illustration, simulated cost analysis is presented here to evaluate the beneﬁt of CO2 enrichment. According to Xu et al. (2010), cost of CO2 for microalgal cultivation is dependent on the source of production of CO2 such as ethanol facilities, hydrogen and ammonia production, gas-processing plants, and fossil power plants. In this illustration, cost of CO2 is considered as 12 USD (ton CO2)1, assuming CO2 is obtained from ethanol production facilities (Xu et al., 2010; Kumar et al., 2011). It is assumed that the caloriﬁc values of algal biomass can be converted into electricity via an internal combustion engine/alternator with an efﬁciency of 60%; and that the price of electricity is 11.58 cents kW h1 (EIA, 2011). Based on the above, the net cost of algal-produced electricity can be estimated by deducting the cost of CO2 from the cost of electricity produced at different CO2-air ratios in the sparging gas.

4.5. Application of the proposed model: optimizing CO2 enrichment -0.6

Several approaches have been suggested in literature to optimize the level of CO2 enrichment in gas-sparged photobioreactors. While some studies have optimized CO2 enrichment with respect to biomass production (Hsueh et al., 2009), few have proposed

0 0

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0.8

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Fig. 6. Simulation of net cost (US cents) and CO2 utilization efﬁciency (%) as a function of CO2-air ratio for N. salina, for two cases: Case 1 – light 200 lE m2 s1; 0.014 g m3; Case 2 – light 200 lE m2 s1; 0.028 g m3.

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Fig. 6 shows the simulated results of net beneﬁt (US cents) and CO2 utilization efﬁciency (%) in two different cases, as a function of CO2-to-air ratios. As CO2-to-air ratio is increased, CO2 utilization efﬁciency decreased continuously, whereas, the net cost increased initially and then declined with further increase in CO2-to-air ratios. For instance, the use of CEA could only be beneﬁcial in case 2 if CO2-to-air ratio could be maintained within 0.1–0.2% based on net beneﬁt. In fact, maximum cost beneﬁt was observed when the CO2-to-air ratio ranged between 0.12% and 0.15%. Thus, the proposed model can be used to regulate the input of CO2 in response to temporal operational variables and culture conditions for optimum CO2 usage. 5. Conclusion The use of airlift column in the open raceway for the supply and transfer of CO2 is modeled, integrating it with a model for predicting biomass growth, incorporating the parameters such as light, CO2, nitrogen and temperature. Predictions of biomass concentrations by the proposed model agreed well with the temporal trend of the experimental data, with r2 ranging from 0.96 to 0.98, p < 0.001. Based on model simulations, the proposed model could prove useful in scaling up and optimizing the input of CO2 in the proposed airlift-raceway conﬁguration in response to temporal operational variables and culture conditions. Acknowledgements This study was supported in part by a Grant from the DOE National Alliance for Advanced Biofuels and Bioproducts (NAABB), a Grant from the US Air Force Research Laboratory (AFRL), by the NSF Engineering Research Center: RenuWIT, and by the Ed & Harold Foreman Endowed Chair. Appendix A. Supplementary material Supplementary material associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.biortech.2013.02.028. References Arudchelvam, Y., Nirmalakhandan, N., 2012. Optimizing net energy gain in algal cultivation for biodiesel production. Bioresour. Technol. 114, 294–302. Becker, E.W., 1994. Microalgae: Biotechnology and Microbiology, ﬁrst ed. Cambridge University Press, New York. Benson, B.C., Maria, T., Wing, G., Rusch, K.A., 2007. The development of a mechanistic model to investigate the impacts of the light dynamics on algal productivity in a Hydraulically Integrated Serial Turbidostat Algal Reactor (HISTAR). Aquacult. Eng. 36, 198–211. Bernard, O., Hadj-Sadok, Z., Dochain, D., Genovesi, A., Steyer, J.P., 2001. Dynamical model development and parameter identiﬁcation for an anaerobic wastewater treatment process. Biotechnol. Bioeng. 75, 424–438. Bischoff, H.W., Bold, H.C., 1963. Phycological Studies in Some Soil Algae from Enchanted Rock and Related Algal Species. University of Texas, Australia, Vol. 6318, pp. 1–95. EIA (Energy Information Administration). 2011. Annual Energy Outlook 2011. U.S. Department of Energy. Falkowski, P.G., 1984. Kinetics of adaptation to irradiance in Dunaliella tertiolecta. Photosynthetica 18, 62–68. Geider, R.J., Osborne, B.A., 1991. Algal Photosynthesis: The Measurement of Gas Exchange and Related Processes. Chapman & Hall, New York, p. 256.

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Further reading Blenke, H., 1979. Loop Reactors. Adv. Biochem. Eng. 13, 121–214.

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