Photobioreactors: light regime, mass transfer, and scaleupychisti/Asterio.pdf · 2002. 2. 1. · Eq. (8) accounts for photoinhibition and the fact that the dependence of m on the

Journal of Biotechnology 70 (1999) 231–247

Photobioreactors: light regime, mass transfer, and scaleup

E. Molina Grima, F.G. Acien Fernandez, F. Garcıa Camacho, Yusuf Chisti *Department of Chemical Engineering, Uni6ersity of Almerıa, E-04071 Almerıa, Spain

Received 7 September 1998; received in revised form 20 November 1998; accepted 22 December 1998

Abstract

Design and scaleup of tubular photobioreactors are discussed for outdoor culture of microalgae. Cultureproductivity is invariably controlled by availability of light, particularly as the scale of operation increases. Thus, lightregime analysis is emphasized with details of a methodology for computation of the internal culture illuminationlevels in outdoor systems. Supply of carbon dioxide is discussed as another important feature of algal culture. Finally,potential scaleup approaches are outlined including promising novel concepts based on fundamentals of theunavoidable light–dark cycling of the culture. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Light regimen; Mass transfer; Microalgae; Photobioreactors; Scaleup

1. Introduction

Although the term ‘photobioreactor’ has beenapplied to open algal ponds and channels, it isbest reserved for devices that allow monosepticculture which is fully isolated from a potentiallycontaminating environment. This latter definingconvention will be followed here. The availablephotobioreactor configurations are numerous(Lee, 1986; Tredici and Materassi, 1992;Borowitzka, 1996; Pulz and Scheinbenbogen,1998), but most may be classified into one of twotypes: either tubular devices or flat panels. Thesecan be further categorized according to orienta-tion of tubes or panels, the mechanism for circu-

lating the culture, the method used to providelight, the type of gas exchange system, the ar-rangement of the individual growth units, and thematerials of construction employed. The develop-mental state of the photobioreactor technologyhas been reviewed comprehensively elsewhere(Lee, 1986; Borowitzka, 1996; Pulz and Schein-benbogen, 1998); here the focus is on tubularphotobioreactors (Fig. 1) which are amongst themost promising culture systems for potentiallarge-scale production of microalgae-derived high-value products. Some potential products are listedin Table 1.

Design and scaleup methodologies for photo-bioreactors are poorly developed. Irrespective ofthe specific reactor configuration employed, sev-eral essential issues need addressing (Weissman etal., 1988): (i) effective and efficient provision of

* Corresponding author. Tel.: +34-950-21-5032; fax: +34-950-21-5484.

E-mail address: [email protected] (Y. Chisti)

0168-1656/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S 0168 -1656 (99 )00078 -4

E. Molina Grima et al. / Journal of Biotechnology 70 (1999) 231–247232

light; (ii) supply of carbon dioxide while minimiz-ing losses; (iii) removal of photosynthetically gen-erated oxygen that may inhibit metabolism orotherwise damage the culture if allowed to accu-mulate; and (iv) sensible scalability of the photo-bioreactor technology.

Biomass productivity of a photobioreactor de-pends on close alignment of the culture environ-ment to the needs of the selected algal strain.Some environmental factors, e.g. temperature andmineral nutrients supply, are relatively easily con-trolled, but others such as the supply of solarradiation are more difficult to regulate. Productiv-ity is determined by the growth rate which, forfixed fluid-dynamics and temperature, is a func-tion of the light profile within the reactor and thelight regime to which the cells are subject. Indense microalgal cultures, light penetration is im-peded by self-shading and light absorption (Rabeand Benoit, 1962; Frohlich et al., 1983; Ericksonand Lee, 1986). These effects affect the radiationprofile inside the culture. Consequently, within aphotobioreactor exist zones of different levels ofillumination. These zones may have different vol-umes. How long the cells reside in zones of differ-ent illumination is a function of the culture

fluid-dynamics (Philliphs and Myers, 1954; Terry,1986; Grobbelaar, 1994; Grobbelaar et al., 1996).In addition to affecting light availability, fluidmovement affects also the transport behavior, i.e.availability of carbon dioxide and other nutrients.In an optimal system where no other factors limit,the light availability determines the rate of photo-synthesis and the productivity. However, excessivelight can be harmful and is known to produce aphotoinhibitory response (Bannister, 1979; Aiba,1982). Here we address the essential aspects ofproviding light to outdoor photosynthetic cul-tures, supplying carbon dioxide as the principalcarbon source, and scaling up of photobioreac-tors, with emphasis on the tubular types.

2. Light regime

2.1. How light affects producti6ity?

Availability and intensity of light are the majorfactors controlling productivity of photosyntheticcultures (Lee and Low, 1992; Pulz and Scheinben-bogen, 1998). In continuous culture as typicallypracticed for microalgae, the biomass productivity

Fig. 1. Airlift-driven tubular photobioreactors. Two reactors are shown with the tubular loops immersed in a pond of cooling water.The two vertical columns at the far end are the airlift devices for circulating the culture through the horizontal loops. The 0.2-m3

photobioreactor on the right was used in obtaining the data presented.

E. Molina Grima et al. / Journal of Biotechnology 70 (1999) 231–247 233

Table 1Potential high–value products from photosyntheticmicroorganismsa

Current or po-Product Source organismb

tential use

Amphidinolides Amphidinium sp. Antitumor agentand amphdinins

Haematococcus plu-Astaxanthin Pigment6ialis, Chlorella sp.

b-Carotene Colorant, foodDunaliellasupplement

Isochrysis galbana Essential fattyDocosahexaenoicacid acid

Essential fattySpirulina sp.g-Linolenic acidacid

Other polyunsatu- Health care,Phaeodactylum tri-cornutum, Isochrysisrated fatty food supplementgalbanaacidsPhaeodactylum tri-Fucoxanthin AntioxidantcornutumAlexandrium hiranoiGoniodomins Antifungal agent

Elastase in-Oscillatoria agardhiiOscillapeptinhibitor

Red algae, ColorantsPhycobiliproteinscyanobacteriaSpirulina platensisPhycocyanin Colorant

a Based on Yamaguchi (1997) and Benemann (1989).b Only representative examples are listed.

els that express m in terms of the average irradi-ance raised to some power greater than unitybetter fit experimental observations (FernandezSevilla, 1995; Pulz and Scheinbenbogen, 1998).Thus, using the previously developed (MolinaGrima et al., 1994) Eq. (7) of Table 2 as a startingpoint, we established the equation (Molina Grimaet al., 1996),

m=mmax·Iav

�b+

c

Io

��

Ik

�1+

�Io

Ki

�a�n�b+c

Io

�+Iav

�b+

c

Io

�. (8)

Eq. (8) accounts for photoinhibition and the factthat the dependence of m on the average irradi-ance (Iav) varies with the incident irradiance level(Io). Eq. (8) was established with an outdoorculture of Phaeodactylum tricornutum UTEX 640(Acien Fernandez et al., 1998); the specific valuesof the various growth parameters for that culture

Table 2Models for light–dependent specific growth rate

Equation Reference

Tamiya et al. (1953)1.m=

ammaxI

mmax+aI(2)

Van Oorschot (1955)2.m=mmax

�1−e

−I

Imax�

(3)

Steele (1977)3.m=

mmaxI

Imax

e�

1−I

Imax

�(4)

4. Bannister (1979)m=

mmaxI

(Kim+Im)

1

m

(5)

Aiba (1982)5.m=

mmaxI

Ks+I+I2

Ki

(6)

Molina Grima et al. (1994)6.m=

mmaxIn

Ikn+In

(7)

(p) is a function of the cell concentration (Cb) inthe effluent and the dilution rate (D); thus,

p=DCb. (1)

At steady state, the dilution rate equals the spe-cific growth rate (m) which is governed by theamount of light, the rate controlling factor. Thedependence of m on the average irradiance hasbeen expressed variously as summarized in Table2. Generally, m increases with increasing irradi-ance, reaching a maximum value, mmax. Furtherincrease in irradiance may actually inhibitgrowth—a phenomenon known asphotoinhibition.

Although photoinhibition is well documented,it has often been disregarded. For example, Eqs.(2)–(4) and Eq. (7) in Table 2 do not take pho-toinhibition into account. In Table 2, only Eq. (5)and Eq. (6) consider the inhibitory effects ofexcessive light. Studies suggest that growth mod-


Table 3Kinetic parameters (Eq. (8)) for an outdoor culture of P.tricornutum (Acien Fernandez et al., 1998)

ValueaParameter

mmax (h−1) 0.06394.3Ik (mE m−2 s−1)

3426Ki (mE m−2 s−1)3.04a1.209b

514.6c

a The noted values apply over the full calendar year.

and Low, 1991, 1992; Quiang et al., 1996; AcienFernandez et al., 1997); the concentration andmorphology of cells; the level of cellular pigmen-tation; and the absorption characteristics of thepigment.

An additional complicating factor is generallyspecific to outdoor culture: Outdoor cultures aresubject to cyclic changes in irradiance levels. Atleast two cycles can be distinguished with substan-tially different cycling times: (i) a relatively longdaily cycle; and (ii) a yet longer cycle based on thechange of seasons during the year. A third cycle isdue to fluid movement between zones of differentillumination within a photobioreactor. Cycles (i)and (ii) affect only the incident radiation on thesurface of a photobioreactor, but beyond thatfactor these cycles are unlikely to have any otherimpact on kinetics of the culture. The period ofcycle (ii) is much longer than the residence time ofthe cells in a photobioreactor in continuous cul-ture. The diurnal cycle means that a culture islight limited at dawn and dusk; however, duringthe midday peak light period, the culture may bephotoinhibited. The peak light level may exceed2000 mE m−2 s−1, which is several times abovethe saturation irradiance. When the external irra-diance level varies with time, an average irradi-ance is determined by time-averaging over shortintervals.

Current methods of estimating an ‘average irra-diance’ level do not take into account the light–dark cycling associated with fluid motion in abioreactor. In reality, light regime experienced bycells, i.e. the total cumulative illumination and thelight–dark movement frequency, is what logicallyshould affect biomass productivity. Identical aver-age irradiance levels cannot necessarily meanidentical productivities: if a culture requires acertain cumulative photon flux density level over a6-h residence time, the same level could be pro-vided over a shorter period without affecting theaverage light level over the residence time interval;however, this is bound to reduce productivity.

Existing methods of estimating average illumi-nation employ an approach consisting of the fol-lowing: (i) estimation of the total photo-synthetically active incident radiation at the sur-face of the photobioreactor; (ii) use of Beer–

are noted in Table 3. Eq. (8) and others in Table2 allow an estimation of the biomass productivityso long as an average irradiance value can bedetermined. This problem is addressed next.

2.2. What is a6erage irradiance?

Even when the outdoor incident radiation levelis constant, the irradiance within a culture variesas a function of position (Erickson and Lee,1986). Cells nearer the light receiving surface ex-perience a higher irradiance than cells elsewhere inthe vessel (Frohlich et al., 1983). Cells closer tothe light source shade those further away; hence,productivity varies with position and time(Tamiya et al., 1953; Bannister, 1979; Laws, 1980;Myers, 1980; Ree and Gotham, 1981). A meanvalue of irradiance may be defined as the volumeaverage of the local irradiance values inside aculture. An average irradiance (Iav) is the lightlevel experienced by a single cell randomly mov-ing inside the culture (Rabe and Benoit, 1962). Ina cell-free system, average irradiance is indepen-dent of the state of mixing. When cells are dis-tributed homogeneously, the average irradianceunder given conditions is again the same for allcells; however, as discussed later, average irradi-ance is not a sufficient criterion of culture perfor-mance because it considers only the total length ofthe dark and the light periods, not the frequencyof switch. Ignoring for the moment the dynamicsof the cell, the average irradiance level (Iav) insideculture depends on the following factors: the ex-ternal irradiance (Io) on the surface of the reactor;the reactor geometry (Frohlich et al., 1983; Lee


Lambert law to determine the radiation level atany depth inside the culture; and (iii) some formof averaging of the radiation level inside the ves-sel. The various method vary in details of steps (i)and (iii). Step (ii) requires measured data on theattenuation of incident radiation with depth; theattenuation is a function of the concentration ofthe cells and the light absorption characteristics ofthe cellular pigments (Chrismadha andBorowitzka, 1994). Some of these steps are dis-cussed later in this overview.

2.3. Quantifying a6erage irradiance

To establish the average irradiance level insidea vessel, we must first determine the incidentirradiance level as discussed below.

2.3.1. Incident radiationThe radiation incident on the surface of a pho-

tobioreactor consists of direct sunlight, reflectedradiation from the surroundings, and diffuse radi-

ation due to particulate matter in the atmosphere.The incident sunlight level is easily estimated (Liuand Jordan, 1960; Duffie and Beckman, 1980).The incident light level on an outdoor reactor is afunction of time, the geographic location of thereactor, and environmental factors (Incropera andThomas, 1978). Principles of solar power engi-neering provide methods for estimation of theincident photon flux anywhere on the surface ofthe Earth (Liu and Jordan, 1960; Duffie andBeckman, 1980) so long as the following areknown: the day of year (N), the solar hour ("),and the geographic latitude (f) of the photobiore-actor. These variables determine the angle of inci-dence (u) of direct radiation on thephotobioreactor’s surface, i.e. the angle betweenthe incident beam and the normal to the surface(Fig. 2). Two additional angles need to be known:the surface slope (b), i.e. the angle between thephotobioreactor’s surface and the horizontal; andthe surface azimuth angle (g), i.e. the deviation ofthe projection on a horizontal plane of the normal

Fig. 2. The various angles relevant to estimation of solar radiation level incident on the flat surface of a photobioreactor with anygeneral orientation relative to the land (see text for details). Adapted from Duffie and Beckman (1980).


to the surface from the local meridian, with zerodue south, east negative, and west positive (Liuand Jordan, 1960; Duffie and Beckman, 1980).Under certain conditions, a culture vessel mayhave multiple values of b and g.

The total daily radiation (H), the daily diffuseradiation (Hd), and the daily direct radiation (HB)on a horizontal surface are all dependent on thelevel of the extraterrestrial radiation (Ho) ob-tained as (Liu and Jordan, 1960)

Ho=�24z

p

��1+0.003·cos

�360N365

��

cos f ·cos d ·sin vs+2pvs

360·sin f ·sin d

�, (9)

where z is the universal solar constant (z=1353W m−2, Duffie and Beckman, 1980) and vs isgiven as (Liu and Jordan, 1960):

vs=cos−1(− tan d ·tan f). (10)

In Eq. (9) and Eq. (10) f is the geographiclatitude and d depends on the day of the year (Liuand Jordan, 1960) as follows,

d=23.45·sin�360(284+N)

365�

. (11)

Now, H, Hd, and HB are, obtained as noted byLiu and Jordan (1960); thus,

H=ÒHo, (12)

Hd= (1.390−4.027Ò+5.530Ò2−3.108Ò3)H,(13)

and

HB=H−Hd. (14)

In these equations, Ò is the atmospheric clarityindex which is a function of factors such as cloudcover and the amount of suspended matter in theatmosphere.

The photosynthetically active amount of thetotal hourly radiation incident (I) on a horizontalsurface is a function of H and the solar hour(Duffie and Beckman, 1980); thus,

I=pHEf

24{[0.409+0.5016·sin(vs−60)]

+ [0.6609−0.4767·(vs−60)]cos v}

×� cos v ·cos vs

sin vs−vs ·cos vs

�, (15)

where the angle v depends on the solar hour (Liuand Jordan, 1960):

v=15(12−'). (16)

In Eq. (15) the factor Ef is the photosyntheticefficiency of the solar radiation and it takes intoaccount the fact that only a part of the total solarspectrum is photosynthetically active. Similarly,the photosynthetically active amount of thehourly diffuse radiation incident (ID) on a hori-zontal surface is obtained as a function of dailydiffuse radiation (Hd) and the solar hour (Duffieand Beckman, 1980):

ID=pHdEf

24� cos v ·cos vs

sin vs−vs ·cos vs

�. (17)

Now, the photosynthetically active direct hourlyradiation level (IB) is obtained as

IB=I−ID. (18)

Eqs. (15)–(18) apply to a horizontal surface.When the surface is tilted, the IB and ID valuesneed to be corrected (Liu and Jordan, 1960); thus,

IBt=IB

cos u

cos uz

, (19)

and

IDt=ID�1+cos b

2�

, (20)

where IBt and IDt are the equivalents of IB and ID

for the surface tilted at angle b relative to thehorizontal. In Eq. (19) u is the angle of incidencewhich, according to Liu and Jordan (1960), iscalculated as

u=cos−1(sin d ·sin f ·cos b

−sin d ·cos f ·sin b ·cos g

+cos d ·cos f ·cos b ·cos v

+cos d ·cos f ·sin b ·cos g ·cos v

+cos d ·sin b ·sin g ·sin v). (21)

The angle uz (Eq. (19)) is estimated as:


uz=cos−1(cos d ·cos f ·cos v+sin d ·sin f). (22)

The level of radiation reflected from theground (Ir) can be estimated using the equation(Liu and Jordan, 1960)

Ir+ (IB+ID)r�1−cos b

2�

, (23)

where r is the ground reflectivity. For the pur-pose of the work discussed here, a ground reflec-tivity (r) value of 0.5 was assumed (GarcıaCamacho et al., 1999). For any three-dimensionalphotobioreactor, the total incident radiation isthe sum of the direct, diffuse, and reflected, i.e.IBt+IDt+Ir ; however, Ir may be ignored for ahorizontal surface such as the top face of a flatplate. Once the photosynthetically active radia-tion incident on the surface of a photobioreactorat a given instant is established (Eqs. (19) and(20), and Eq. (23)), the next step is to determinethe local radiation level as a function of positioninside the culture. This is explained in the follow-ing section.

2.3.2. Local irradianceEven though the fluid in a photobioreactor

may be well-mixed and with uniform opticalproperties, the illumination profile within is neveruniform even when the culture depth is quiteshallow. The irradiance at any point in the cul-ture is a function of the total incident radiationat the surface of the culture, the optical proper-ties of the culture, and the distance that thepoint is located from the surface. The mathemat-ical relationship governing the local irradiance isthe well-known Beer–Lambert law.

For any photobioreactor, the distance (Pdirect)traveled by a direct ray from the tube’s surfaceto a point within the culture may be determinedfrom the position of the Sun, which establishesthe point of incidence on the surface of the reac-tor, and the polar coordinates of the point (ri, 8)in a cross-section of the tube. For a vertical tubeas illustrated in Fig. 3, the distance (Pdirect) to thepoint (ri, 8) is calculated as (Garcıa Camacho etal., 1999),

Fig. 3. Relationships among the various angles and distancesassociated with the path of direct radiation to any internalpoint (ri, 8) inside the culture in a vertical tube. A plan viewof the cross-section of the tube is shown in the lower part ofthe figure.

Pdirect=ai ·cos v

cos�p

2−u z%

�=R ·sin o−ri sin 8

cos�p

2−u z%

� , (24)

where the parameter ai is

ai

ri cos 8−R ·cos o

sin v=

R ·sin o−ri sin 8

cos v. (25)

The various lengths and angles relevant to Eq.(24) and Eq. (25) are shown in Fig. 3. The angleu z% in Eq. (24) is a function of the refractiveindices of air and water; using Snell’s law, u z% canbe shown to be:

u z%=sin−1(0.752·sin uz). (26)

Once, the distance to the point (Pdirect) is deter-mined, Beer–Lambert law may be applied to ob-tain the local irradiance IBt(ri, 8); hence,

IBt(ri, 8)=IBt exp(−KaCbPdirect), (27)


where Ka is the absorption coefficient and Cb isthe concentration of biomass. Eq. (27) is writtenfor the direct radiation; similar equations may bewritten for the disperse radiation and reflectedradiation. The local value of IDt at location (ri, 8)is given as

IDt(ri, 8)=IDt exp(−KaCbPdisperse), (28)

where, based on trigonometric principles, thePdisperse can be shown to be

Pdisperse

=(ri sin 8−R ·sin o)2+ (ri cos 8−R ·cos o)2.(29)

The computed local irradiance profiles in ahorizontal and an equal-diameter vertical tube atsolar hours 8 and 12 are shown in Fig. 4. Asexpected, in both cases, the local irradiance profi-les change with the changing position of the Sun.In the morning ("=8), in the vertical reactor theside facing the Sun had much higher direct localirradiance values than the opposite side. This

difference was lower in the horizontal reactor.However, at noon, the irradiance distribution inthe vertical vessel, unlike the horizontal tube, wasfairly homogeneous, i.e. the local irradiance valuedid not depend on the angle 8. The reason forthis phenomenon follows: around midday, thecontribution of the dispersed irradiance to thetotal irradiance is large in comparison with thecontribution of the direct irradiance in the verticalarrangement. Clearly, the level of irradiance isalways higher in the horizontally placed tube irre-spective of the solar hour.

Once the local irradiance has been established,the average irradiance is calculated as explainednext.

2.3.3. A6erage irradianceOnce the local direct and local disperse irradi-

ances—i.e. IBt(ri, 8) and IDt(ri, 8), respectively—are estimated, the integration of the local valuesover the length and the radius of the tube yieldsthe total average hourly irradiance inside the cul-ture (Acien Fernandez et al., 1997); thus,

Fig. 4. Calculated radial irradiance profiles in cross-sections of vertical (dashed lines) and horizontal tubes (solid lines) at solar hours8 and 12. Both tubes were 0.1 m in diameter; the assumed biomass concentration was 1.9 kg m−3 of P. tricornutum with a pigmentcontent of 2.21%.


Iav=1

pR2

!�&R

&8

IBt(ri, 8) r dr d8�

+� 1

2p

&R

&8

&o

IDt(ri, 8) r dr d8 do�"

. (30)

The foregoing procedure disregards movementof cells among zones of different illumination. Ineffect, the above procedure assumes that the lightexposure history of all cells is identical and fre-quency of light–dark movement is inconsequen-tial. The first of these assumptions is generallyvalid in a given vessel. Furthermore, because thelight–dark frequency is virtually constant in agiven flow regime for a specific reactor, effects ofthe light–dark movement are masked in a givenreactor; however, problems arise when comparingreactors of different scales. This aspect is exam-ined in the section on scaleup.

3. Gas–liquid mass transfer: provision of carbondioxide

Carbon dioxide is the usual carbon source forphotosynthetic culture of microalgae. Carbondioxide is typically supplied by continuous orintermittent injection of the gas at the beginningof a tubular solar receiver. As the carbon isconsumed, oxygen is ultimately produced by pho-tolysis of water. The generated oxygen is releasedinto the culture fluid. The fluid in a tubular solarreceiver is invariably in plug flow; hence, theconcentration of carbon dioxide reflected in theculture pH changes (Livansky and Bartos, 1986)along the tube and so does the concentration ofoxygen (Weissman et al., 1988). Gas–liquid masstransfer in such a system has been addressed(Camacho Rubio et al., 1999) following similardevelopments for open raceway culture (Livansky,1982, 1990; Livansky and Bartos, 1986).

For the liquid phase in plug flow, the changesin concentrations of dissolved oxygen and dis-solved inorganic carbon along the loop are ex-pressed as follows (Camacho Rubio et al., 1999):

QL d [O2]= (kLaL)O2([O2]*− [O2])Sdx

+RO2(1−oG)Sdx, (31)

QL d [CT ]= (kLaL)CO2([CO2]*− [CO2])Sdx

+RCO2(1−oG)Sdx, (32)

where QL is the volumetric flow rate of liquidthrough the tube, kLaL is the volumetric gas–liq-uid mass transfer coefficient, Sdx is the differen-tial volume of the tube, and oG is the fractionalgas holdup. The volumetric rates of generation ofoxygen and consumption of carbon dioxide arerepresented as RO2

and RCO2, respectively. The

liquid phase concentrations of oxygen, inorganiccarbon, and carbon dioxide are represented as[O2], [CT], and [CO2], respectively. Note that theconcentration values marked with asterisks areequilibrium concentrations, i.e. the maximum pos-sible liquid–phase concentration of the compo-nent in contact with the gas phase of a givencomposition. In Eq. (31) and Eq. (32), the firstterm on the right-hand-side accounts for masstransfer to/from the gas phase and the secondterm accounts for generation or consumption.

Depending on the situation, any of the termson right-hand-side of Eq. (31) and Eq. (32) maybe positive or negative. The mass balance consid-ers the total inorganic carbon concentration [CT]and not just that of carbon dioxide. This is be-cause CT includes the dissolved carbon dioxide,the carbonate (CO3

2−) and the bicarbonate(HCO3

−) species (Livansky, 1990). The CT value ispH dependent as detailed later.

As for the liquid phase, a component massbalance can be established also for the gas; hence,

dFO2= − (kLaL)O2

([O2]*− [O2])Sdx, (33)

and

dFCO2= − (kLaL)CO2

([CO2]*− [CO2])Sdx, (34)

where FO2and FCO2

are the molar flow rates of thetwo components in the gas phase. Note that be-cause of the changes in molar flow rates, thevolumetric flow rate of the gas phase may changealong the tube. This change is easily evaluatedfrom the available equations of state for gases.This analysis assumes a constant molar flow ratefor nitrogen and water within any section of thetube: nitrogen is neither consumed nor generated,and the gas phase is water saturated.


The equilibrium concentrations of the two gasesin the liquid can be calculated using Henry’s law;thus,

[O2]*=HO2PO2

=HO2(PT−P6)

FO2

FO2+FCO2

+FN2+FH2O

,

(35)

[CO2]*=HCO2PCO2

=HCO2(PT−P6)

FCO2

FO2+FCO2

+FN2+FH2O

,

(36)

where HO2and HCO2

are the Henry’s constants foroxygen and carbon dioxide. The other symbolsare explained in the nomenclature.

Eqs. (31)–(36), in combination with the knowninitial conditions and the dissociation equilibriafor water and H2CO3, allow the determination ofthe CO2 and O2 axial profiles in the tubular loop.Similar methods have been applied to other zonesof a photobioreactor, e.g. the riser, the down-comer, and the gas–liquid separating region ofthe airlift device that moves the fluid through thetubular solar loop (Camacho Rubio et al., 1999).

As noted earlier, the total inorganic carbonconcentration and the dissolved carbon dioxide inthe culture are interrelated (Livansky, 1990). Thedissolved carbon dioxide is in equilibrium withcarbonate and bicarbonate species. These equi-libria are pH dependent (Livansky and Bartos,1986). The pH variation in culture is mainly dueto consumption of carbon dioxide although varia-tions due to consumption of other nutrients and/or degradation of the excreted metabolites occur.Loss of dissolved carbon dioxide due to uptakeinto algal cells is partly compensated by regenera-tion from carbonates and bicarbonates (Livansky,1990). Consequently, carbon dioxide uptake isaccompanied by changes in pH. The total concen-tration of inorganic carbon is given by:

[CT]= [CO2]+ [HCO3−]+ [CO3

2−]. (37)

Using Eq. (37) and the well-known dissociationequilibria for water and carbonate–bicarbonatesystem (Livansky, 1990), we obtain,

[CT]=�

1+K1

[H+]+

K1K2

[H+]2�

[CO2], (38)

where K1 and K2 are the first and second dissocia-tion constants for H2CO3. Eq. (38) can be rewrit-ten in a differential form as follows,

d[CT]

=�

1+K1

[H+]+

K1K2

[H+]2�

d[CO2]

− [CO2]� K1

[H+]2+

2K1K2

[H+]3�

d[H+]. (39)

Taking into account the electroneutrality con-straint, the well-known dissociation equilibria forwater and H2CO3, and assuming a constant con-centration of all ions other than H+, OH−, car-bonate, and bicarbonate in the culture, thefollowing is easily derived (Camacho Rubio et al.,1999):

d[H+]

=

K1

[H+]+

2K1K2

[H+]2

1+Kw

[H+]2+

K1[CO2][H+]2

+8K1K2[CO2]

[H+]3

d[CO2].

(40)

Eq. (39) and Eq. (40) relate the three concentra-tions, [H+], [CT] and [CO2]; hence, any two ofthose concentrations may be calculated if thethird is known.

Similar mass transfer models exist for openchannel type algal culture systems (Livansky,1982, 1990; Livansky and Bartos, 1986; Markland Mather, 1985). The noted model is potentiallyuseful for limited scaleup; it does not considerpossible inhibitory effects of accumulated oxygenon photosynthesis, i.e. RO2

and RCO2are assumed

to be axially invariant and possible changes in cellconcentration are disregarded. Furthermore, in along tube, other parameters (e.g. gas holdup andkLaL) are likely to also vary.

Camacho Rubio et al. (1999) used Eqs. (31)–(40) for estimating the behavior of a culture sys-tem. Culture variables such as dissolved oxygen,carbon content in the fluid, the composition of theoutlet gas, the carbon dioxide requirements, andthe pH of the culture could be predicted. As


Fig. 5. Predicted (solid lines) and measured values of thefollowing variables: dissolved oxygen at the end of the tubularloop (top figure); oxygen and carbon dioxide mole fractions inthe exit gas (middle figure); carbon dioxide losses in theexhaust gas and the culture pH (lower figure). All variables areshown as functions of solar hour. The predictions (continuouslines) are based on the mass transfer model described (Cama-cho Rubio et al., 1999).

earlier; however, because the solar receiver tubesof the photobioreactor were located in a coolingpond that had a radiation concentrating effect(albedo=2), the incident radiation level was ap-propriately corrected (Acien Fernandez et al.,1998). The efficiency factor Ef (Eq. (15)) valueused was 1.7490.07 mE J−1 as previously dis-cussed (Acien Fernandez et al., 1998).

4. Scaleup

No reliable systematic scaleup method exists forphotobioreactors. The mass transfer and the lightregimen models outlined above provide a usefulstarting point as detailed elsewhere (Camacho Ru-bio et al., 1999). Predictive capability of the notedmass transfer model has been confirmed for arange of parameters (Camacho Rubio et al.,1999); however, as noted in the previous section,because of several restrictive assumptions, themodel could not a priori predict the performanceof a significantly larger reactor particularly if thetube diameter changed substantially. This point isimportant: other than ‘scaleup’ by multiplicationof identical tubular modules, the only way toincrease volume is by increasing length or/anddiameter. Nevertheless, simulations based on themass transfer model (Camacho Rubio et al., 1999)suggest that increasing tube length for a constantdiameter will alter the culture pH at the tube exit,the dissolved oxygen content of the exiting fluid,and the carbon dioxide losses as shown in Fig. 6.The vertical bars around the simulated profiles inFig. 6 indicate the maximum expected changewhen the air flow rate in the airlift pump is variedover 25–45 l min−1, the injection rate of carbondioxide/air mixture for pH control varies over70–110 l h−1, and the composition of the pHcontrol gas mixture is changed to contain 0.4–1.0mole fraction of carbon dioxide (Camacho Rubioet al., 1999). The predictions in Fig. 6 disregardany inhibition of photosynthesis due to accumula-tion of oxygen and any change in culture irradi-ance due to buildup of biomass.

Unlike the predictions in Fig. 6, a plug flowreactor scaled up using established methodsshould have the same exit composition (oxygen

shown in Fig. 5, through any 24-h period, themodel predictions agreed closely with the mea-surements; hence, demonstrating the predictivecapability of the model. The data in Fig. 5 wereobtained during an outdoor culture of P. tricornu-tum (Camacho Rubio et al., 1999). An airlift-driven tubular photobioreactor was employed(Fig. 1) as detailed previously (Acien Fernandez etal., 1998). The average light level in the culturewas established using the methodology outlined


content, carbon dioxide content, biomass concen-tration) as a smaller device: normally, in scalingup a plug flow reactor, the highest practicabledilution rate—i.e. the minimum residence timefor a given exit biomass concentration—is estab-lished at a small scale. The same value of resi-dence time applies to a longer tube of the samediameter as the smaller one; thus, the flow veloc-ity in the longer pipe must be greater by a factorof length ratios of the larger-to-smaller tubes.Adhering to this criterion ensures that propertiesof the product stream leaving the longer tubematch those established at the smaller scale.When this criterion is followed, all of the concen-tration profiles in the direction of flow will beidentical at both scales. In any event, mass trans-fer of carbon dioxide and oxygen are not theprincipal factors limiting scalability. Supply ofcarbon dioxide is relatively easily managed irre-spective of scale, whereas build-up of oxygen toinhibitory levels is a far lesser problem than ade-quacy of illumination.

Unless the tubular reactor is scaled up bychanging the length, any change in dimensionswould imply a change in the relative volumes ofthe light and dark zones: under given conditions(external illumination, cell concentration, pigmentcontent), the depth at which light intensity de-clines to a growth limiting level will not be af-fected, but the diameter of the dark zone will

increase. Performance of a reactor will change onscaleup—it will deteriorate unpredictably—un-less the frequency of light–dark interchange offluid is held constant upon scaleup. If the light–dark cycling time is allowed to increase with scaleof operation, the reactor productivity will begin todecline as soon as the cycling time exceeds amaximum value, roughly the equivalent of thetime interval between uptake of photons by thephotosynthetic machinery when the light is avail-able at saturation intensity or slightly higher.Data exists on the acceptable frequency of light–dark cycling for some algae and can be easilydetermined for others (Philliphs and Myers, 1954;Grobbelaar, 1994; Grobbelaar et al., 1996). Incontrast, there is no information on the frequencyof light–dark interchange of fluid in bioreactors,except in laminar flow when any radial inter-change in a tube would be solely by diffusion orin effect no radial movement.

Several approaches have been suggested forquantifying the light–dark cycling of fluid in abioreactor. One approach relies on analogy withmass or heat transfer from the wall of a tube tothe turbulently flowing fluid (Merchuk et al.,1998). In principle, available mass or heat transfercorrelations could be used to determine a transfercoefficient. The latter could be used to determinea surface renewal time at the tube wall followingthe concepts of the classical surface renewal the-

Fig. 6. Model predicted values of carbon dioxide loss, the culture pH, and the dissolved oxygen concentration at tube exit forvarious lengths of the tubular loop (Camacho Rubio et al., 1999).


ory of transport. This method would be valid onlyif the depth of the light zone was of the sameorder as the laminar boundary layer at the wall ofthe tube. The depth of the boundary layer is ofthe order of cellular dimensions; hence, this ap-proach is entirely unrealistic except, possibly, inexceedingly dim light.

Another similar approach relies on the velocityof the turbulent microeddies in the fluid. The eddyvelocity u is easily determined using the well-known Kolmogoroff’s model of turbulence;hence,

u=�mLj

rL

�1

4, (41)

where rL is the density of the fluid, mL is itsviscosity, and j is the energy dissipation rate perunit mass calculated as,

j=2CfUL

3

d. (42)

In Eq. (42) UL is the superficial liquid velocity, Cf

is the Fanning friction factor, and d is the hy-draulic diameter of the tube. Again, the calculatededdy velocity would be a measure of the light–dark cycle if the depth of the dark zone equaledthe dimensions of the microeddies. The latter arequite small, usually less than 200 mm; thus, theapproach is plainly unsound as a measure of thelight–dark frequency in tubular photobioreactors.

An alternative approach, not yet fully devel-oped, follows. For any tube of diameter dT, thedepth of the light zone dL can be calculated byapplying Beer–Lambert law for known level ofexternal incident illumination, the biomass con-tent, the absorption coefficient, and the saturationirradiance value. Assuming a homogeneous exter-nal illumination, the depth of the dark zone in thetube becomes

dk=dT−2dL. (43)

Thus, the volume of the dark zone per unit tubelength is

Dark volume=p(dT−2dL)2

4. (44)

If ud is the maximum acceptable duration of thedark period between successive light periods, then

the maximum residence time of fluid in the darkzone should be 5ud. Therefore, the volumetricrate of fluid movement out of the dark zone is

QR=dark zone volume

ud

=p(dT−2dL)2

4ud

. (45)

This QR value is on a unit tube length basis.Because all the fluid moving out of the dark zonemust pass through the boundary between the lightand dark zones, a fluid interchange velocity canbe defined as

UR=QR

pdk

=(dT−2dL)

4ud

; (46)

thus,

ud=dk

4UR

. (47)

Increasing scale by increasing diameter does notchange dL for otherwise fixed conditions; only dk

changes. To ensure identical performance at thetwo scales, the scaleup criterion becomes� dk

4UR

�large

=� dk

4UR

�small

, (48)

or

dkL

dkS

URS

URL

=1, (49)

where the subscripts S and L refer to small andlarge scales, respectively. If the scale factor is f,i.e. dkL= f ·dkS, then for identical performance, thelarge scale interchange velocity should be

URL= fURS, (50)

where f\1. The radial flow velocities may beestimated from radial dispersion coefficients inturbulent flow; hence

UR8DR

dT

. (51)

Radial dispersion coefficients can be measuredusing suitably designed experiments. Correlationswould need to be established for such dispersioncoefficients as functions of the linear flowReynolds number.

In practice, radial flow may be enhanced bydeploying static mixers inside a tube (Chisti,1998). These mixers should be minimally intrusive


and should be confined to well within the darkcore. One possibility is the use of a coaxiallylocated rod with suitably spaced barbs or projec-tions that have a somewhat flat profile and aresuitably angled to direct the flow into the annularlight zone. The projections should not extend intothe light zone to prevent any loss of illuminationin that zone. If for an algal species, the acceptablecontinuos dark time ud is infinitesimally short,then scaleup without loss of productivity wouldbe impossible by increasing the tube diameter. Intheory, exceedingly high levels of turbulence andhigh radial velocities can be generated. In prac-tice, an upper limit would be encountered at muchlower than technically possible levels of turbu-lence in view of the known algal sensitivity tohydrodynamic shear and limited pressure toler-ance of the typically employed transparent materi-als of construction. In addition, higher airliftdevices would be necessary to generate higherflows through the tubes while compensating forthe significant pressure drop due to static mixingelements (Chisti, 1989; Chisti et al., 1990).

5. Concluding remarks

Of the many types of photobioreactors pro-posed for closed monoculture, tubular devices areamongst the more scaleable and suited to large-scale production. Unlike the widely used openculture systems, the design of closed tubular pho-tobioreactors is more complex. Irradiance levels inculture can be predicted as discussed. Similarly,carbon dioxide supply problems are relatively eas-ily resolved. Difficulties arise with scaleup becauserelative volumes of light and dark zones change asthe tube diameter increases; however, promisingnew leads in this area suggest that dependablescaleup based on fundamental principles shouldbecome feasible in the foreseeable future. Atpresent the recommended method is to use a pipediameter of no more than 0.1 m, and a continu-ous run length of about 80 m with a flow velocityof 0.3–0.5 m s−1. Multiple parallel run tubesoriginating and ending in common headers areapparently the best way to accommodate higherflows and volumes.

6. Nomenclature

a parameter in Eq. (8)path length parameter definedai

by Eq. (25) (m)parameter in Eq. (8)b

Cb biomass concentration (kg m−3)Fanning friction factorCf

CT total inorganic carbon in theliquid (mol m−3)

c parameter in Eq. (8)dilution rate (s−1)D

DR radial dispersion coefficient(m2 s−1)diameter or hydraulic diameterd(m)

dT tube diameter (m)diameter of dark zone (m)dk

diameter of dark zone at largerdkL

scale (m)diameter of dark zone atdkS

smaller scale (m)dL depth of light zone (m)

photosynthetic efficiency of theEf

solar radiation (=1.7490.07mE J−1)carbon dioxide molar flow rateFCO2

in the gas phase (mol s−1)FO2

oxygen molar flow rate in thegas phase (mol s−1)molar flow rate of water in theFH2O

gas phase (mol s−1)FN2

nitrogen molar flow rate in thegas phase (mol s−1)

f scale factortotal daily radiation on a hori-Hzontal surface (J m−2 day−1)daily direct radiation on a hori-HB

zontal surface (J m−2 day−1)HCO2

Henry’s law constant for car-bon dioxide (mol m−3 atm−1)

Hd daily diffuse radiation imping-ing on a horizontal surface(J m−2 day−1)daily global extraterrestrial so-Ho

lar radiation (J m−2 day−1)Henry’s law constant for oxy-HO2

gen (mol m−3 atm−1)


" solar hour (h)hourly incident photosyntheticIradiation on a horizontal sur-face (mE m−2 s−1)photosynthetically active hourlyIav

average irradiance inside culture(mE m−2 s−1)hourly PA direct irradiance onIB

a horizontal surface(mE m−2 s−1)direct hourly PA irradiance onIBt(g, v)a vertical surface (mE m−2 s−1)direct local hourly PA irradi-IBt(ri, 8)ance inside vertical column(mE m−2 s−1)

ID hourly PA diffuse irradianceon horizontal surface(mE m−2 s−1)

IDt hourly PA diffuse irradiance oninclined surface (mE m−2 s−1)disperse hourly PA irradianceIDt(v)on vertical surface (mE m−2 s−1)local hourly disperse PA irradi-IDt(ri, 8)ance inside vertical column(mE m−2 s−1)microalgal affinity for lightIk

(mE m−2 s−1)Imax saturation value of I

(mE m−2 s−1)solar PA irradiance impingingIo

on the reactor’s surface (IBt+IDt) (mE m−2 s−1)hourly reflected PA irradianceIr

on a surface (mE m−2 s−1)absorption coefficient (m2 g−1)Ka

K1 first dissociation constant forH2CO3 (mol m−3)

K2 second dissociation constant forH2CO3 (mol m−3)photoinhibition constantKi

(mE m−2 s−1)saturation constantKs

(mE m−2 s−1)dissociation constant for waterKw

(mol2 m−6)volumetric gas–liquid mass(kLaL)CO2

transfer coefficient for carbondioxide (s−1)

(kLaL)O2volumetric gas–liquid masstransfer coefficient for oxygen(s−1)tube length (m)Lexponent in Eq. (5)mday of the yearNexponent in Eq. (6)n

PA photosynthetically activep biomass productivity

(kg m−3 s−1)carbon dioxide partial pressurePCO2

in the gas phase (atm)Pdirect distance traveled by a direct in-

cident ray from the tube’s surf-ace to any internal point (ri, 8)(m)

Pdisperse distance traveled by disperse ra-diation from the tube’s surfaceto any internal point (ri, 8) (m)oxygen partial pressure in thePO2

gas phase (atm)total pressure in the systemPT

(atm)P6 partial pressure of water vapor

(atm)volumetric liquid flow rateQL

(m3 s−1)volumetric flow rate out ofQR

dark zone (m3 s−1)R radius or hydraulic radius (m)

carbon dioxide consumptionRCO2

rate (mol CO2 m−3 s−1)oxygen generation rate (molRO2

O2 m−3 s−1)r radial distance (m)ri distance in polar coordinates

(m)cross-sectional area of the tubeS(m2)superficial liquid velocity in theUL

tube (m s−1)fluid interchange velocityUR

(m s−1)fluid interchange velocity atURL

larger scale (m s−1)fluid interchange velocity atURS

smaller scale (m s−1)u eddy velocity defined by Eq.

(41) (m s−1)


distance in the direction of flowx(m)

[ ] liquid phase molar concentra-tion of species in brackets(mol m−3)

liquid phase equilibrium con-[ ]*centration of species inbrackets (mol m−3)

6.1. Greek symbols

parameter in Eq. (2)a

surface tilt angle relative to the horizontalb

g surface azimuth angle (−180°5g5180°)d declination of the angular position of the

Sun at solar noon with respect to theplane of the equator, north positive(−23.45°5d523.45°), defined by Eq.(11)

o angle shown in Fig. 3fractional gas holdupoG

angle of incidence defined by Eq. (21)u

angle u modified by refraction in theu %culture

ud maximum duration of dark period (s)zenith angle of the Sun, defined by Eq.uz

(22)zenith angle of the Sun modified by re-u z%fraction in the culture

m specific growth rate (s−1)mL viscosity of liquid (Pa s−1)

maximum specific growth rate (s−1)mmax

energy dissipation rate per unit massj

(W kg−1)p pir ground reflectivity

density of liquid (kg m−3)rL

geographic latitudef

angular position in polar coordinates8

angle corresponding to the solar hour,v

defined by Eq. (16)hour angle at sunrise, defined by Eq. (10)vs

atmospheric clarity index estimated atÒ0.7499%universal solar constant (z=1353z

W m−2)

Acknowledgements

Some of the work described was supported bythe Comision Interministerial de Ciencia y Tec-nologıa, C.I.C.Y.T., Spain (Project Bio 95-0652)and the European Union (Project BRPR CT97-0537).

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Photobioreactors: light regime, mass transfer, and scaleupychisti/Asterio.pdf · 2002. 2. 1. · Eq. (8) accounts for photoinhibition and the fact that the dependence of m on the