Design of static mixers for inclined tubular photobioreactors

Static mixers, which improve gas-liquid mass transfer inside tubular photobioreactors and move the cells between the upper and lower parts of the tubes were designed. Each static mixer was equipped with an opening (v-cut slit) at the top (for gas dispersion) and an orifice at the lower part (for liquid circulation). When the static mixers were installed in the riser tube of an inclined tubular photobioreactor, vertical movement of the liquid was induced so that cells were moved between the surface and bottom part of the photobioreactor. The mass transfer rates in the tubular photobioreactor without static mixers decreased sharply when they were scaled up by increasing the tube diameters. However, by installation of static mixers, the mass transfer rates in 12.5-cm diameter tubes were almost as high as those of 3.8-cm tubes without static mixers. The effectiveness of the static mixers in improving the mass transfer characteristics of the tubular photobioreactors was higher in large than small diameter tubes. The ratio of the diameters of the static mixers to the diameter of the tube, the areas of the v-cut slits and the orifice were the important design parameters that affected the mass transfer characteristics. The gas hold up and and k_La were higher when the areas of the slits (v-cut) and the orifice were reduced.     

Enhancement of mass transfer characteristics and phenanthrene degradation in a two-phase partitioning bioreactor equipped with internal static mixers

Oxygen and substrate supply have always been considered physical constraints for the performance and operation of two-phase partitioning bioreactors (TPPB), widely used for the degradation of hydrophobic substrates. In this regard, the potential advantages of static mixers in upgrading the oxygen transfer and liquid-liquid dispersions in TPPB have been highlighted. In the present paper, the concomitant influence of static mixers on the gas-liquid mass transfer coefficient k _L a and on substrate bioavailability was examined in TPPB. The static method based on conventional forms was developed to estimate the oxygen volumetric mass transfer coefficient. Over a broad range of liquid and air flow rates, the presence of static mixers was found to significantly enhance k _L a relative to a mixer-free mode of operation. For identical conditions, static mixers improved the k _L a threefold. In the presence of external aeration supply, the boost in the k _L a was associated with an increase of 16% in the phenanthrene biodegradation rate due to bubble break up accomplished by the static mixers. On the other hand, static mixers were efficient in enhancing substrate bioavailability by improving the liquid-liquid interfacial area. This effect was reflected by a threefold increase in the degradation rate in the bioreactors with no external supply of air when equipped with static mixers.     

Improving mass transfer in an inclined tubular photobioreactor

The mass transfer and hydrodynamics of two outdoor tubular photobioreactor designs were compared, a Tredici-design near-horizontal tubular photobioreactor (NHTR) and an enhanced version of this reactor (ENHTR), for the purpose of improving algal growth via improved hydrodynamics. The enhancements included addition of vertical bubble columns at the sparger end and a larger degasser with a diffuser. Gas-liquid mass transfer and other performance measures were assessed for a range of gas sparging rates. The ENHTR modifications proved to be very successful, increasing oxygen stripping and carbon dioxide dissolution by 120–220 % and 0–50 %, respectively. There was an increase in axial mixing and a fourfold decrease in total mixing time. Experiments were conducted to determine that approximately 50 % of the mass transfer occurred in the vertical bubble columns, while 85–90 % of the mass transfer in the near-horizontal tubes occurred in the lower half of the tubes. These improvements can lead to increased algae productivity depending upon culture-specific parameters. The theoretical maximum productivity of a hypothetical algal culture would be 1.6 g m^?2 h^?1 in the NHTR, and we have previously achieved a maximum of 1.5 g m^?2 h^?1 growing Arthrospira at densities up to 7.5 g L^?1 in this reactor. Due to enhanced mass transfer in the ENHTR, the predicted maximum productivity should increase to 4.75 g m^?2 h^?1. The potential for further improvements in productivity due to various additional enhancements is described.     

Study of hydrodynamic characteristics in tubular photobioreactors

In this work, the hydrodynamic characteristics in tubular photobioreactors with a series of helical static mixers built-in were numerically investigated using computational fluid dynamics (CFD). The influences of height and screw pitch of the helical static mixer and fluid inlet velocity on the cell trajectories, swirl numbers and energy consumption were examined. In order to verify the actual results for cultivation of microalgae, cultivation experiments of freshwater Chlorella sp. were carried out in photobioreactor with and without helical static mixer built-in at the same time. It was shown that with built-in helical static mixer, the mixing of fluid could be intensified, and the light/dark cycle could also be achieved which is of benefit for the growth of microalgae. The biomass productivity of Chlorella sp. in tubular photobioreactor with helical static mixer built-in was 37.26 % higher than that in the photobioreactor without helical static mixer.     

Outdoor helical tubular photobioreactors for microalgal production: modeling of fluid-dynamics and mass transfer and assessment of biomass productivity

The production of the microalga Phaeodactylum tricornutum in an outdoor helical reactor was analyzed. First, fluid dynamics, mass-transfer capability, and mixing of the reactor was evaluated at different superficial gas velocities. Performance of the reactor was controlled by power input per culture volume. A maximum liquid velocity of 0.32 m s(-1) and mass transfer coefficient of 0.006 s(-1) were measured at 3200 W m(-3). A model of the influence of superficial gas velocity on the following reactor parameters was proposed: gas hold-up, induced liquid velocity, and mass transfer coefficient, with the accuracy of the model being demonstrated. Second, the influence of superficial gas velocity on the yield of the culture was evaluated in discontinuous and continuous cultures. Mean daily values of culture parameters, including dissolved oxygen, biomass concentration, chlorophyll fluorescence (F(v)/F(m) ratio), growth rate, biomass productivity, and photosynthetic efficiency, were determined. Different growth curves were measured when the superficial gas velocity was modified-the higher the superficial gas velocity, the higher the yield of the system. In continuous mode, biomass productivity increased by 35%, from 1.02 to 1.38 g L(-1) d(-1), when the superficial gas velocity increased from 0.27 to 0.41 m s(-1). Maximal growth rates of 0.068 h(-1), biomass productivities up to 1.4 g L(-1) d(-1), and photosynthetic efficiency of up to 15% were obtained at the higher superficial gas velocity of 0.41 m s(-1). The fluorescence parameter, F(v)/F(m), which reflects the maximal efficiency of PSII photochemistry, showed that the cultures were stressed at average irradiances within the culture higher than 280 microE m(-2) s(-1) at every superficial gas velocity. For nonstressed cultures, the yield of the system was a function of average irradiance inside the culture, with the superficial gas velocity determining this relationship. When superficial gas velocity was increased, higher growth rates, biomass productivities, and photosynthetic efficiencies were obtained for similar average irradiance values. The higher the superficial gas velocity, the higher the liquid velocity, with this increase enhancing the movement of the cells inside the culture. In this way the efficiency of the cells increased and higher biomass concentrations and productivities were reached for the same solar irradiance.     

Oxygen transfer and axial dispersion in an aeration tower containing static mixers

Oxygen transfer from gas to liquid under steady-state cocurrent flow conditions was modeled using the dispersion model, and the oxygen transfer coefficients were estimated from available data for a column with Koch motionless mixers. The dispersion in the column was estimated for several different gas and liquid flow rates using steady-state tracer experiments. The estimated oxygen transfer coefficients were compared with those estimated using complete mixing and plug flow models. The results indicate that the dispersion model is the most appropriate model for estimating the mass transfer coefficient from the available data.     

A Simple and reliable formula for assessment of maximum volumetric productivities in photobioreactors

This article establishes and discusses the consistency and the range of applicability of a simple but general and predictive analytical formula, enabling to easily assess the maximum volumetric biomass growth rates (the productivities) in several kinds of photobioreactors with more or less 15% of deviation. Experimental validations are performed on photobioreactors of very different conceptions and designs, cultivating the cyanobacterium Arthrospira platensis, on a wide range of volumes and hemispherical incident light fluxes. The practical usefulness of the proposed formula is demonstrated by the fact that it appears completely independent of the characteristics of the material phase (as the type of reactor, the kind of mixing, the biomass concentration…), according to the first principle of thermodynamics and to the Gauss‐Ostrogradsky theorem. Its ability to give the maximum (only) kinetic performance of photobioreactors cultivating many different photoautotrophic strains (cyanobacteria, green algae, eukaryotic microalgae) is theoretically discussed but experimental results are reported to a future work of the authors or to any other contribution arising from the scientific community working in the field of photobioreactor engineering and potentially interested by this approach. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Intensification of transfer processes in biotechnology and chemical engineering using static mixers. (Review)

A review of the intensification of moment, mass and heat transfer using an “unconventional” method, namely the application of static mixers, also known as “motionless mixers”, is presented in this paper. After the presentation of some structural types of static mixers, studies with particular emphasis on flow behaviour, pressure drop, mixing, mass and, heat transfer in the presence of static mixing devices, used in biotechnology and chemical engineering, were discussed. The suitability of static mixers to enhance the transfer process parameters was also justified by the low energy requirement, while the fluids might have different viscosities and because of this fact they could remove any mistakes made by the equipment. The article is not directed towards a comprehensive review, but it should serve as a landmark in future undertakings.     

Hydrodynamics and mass transfer in a tubular airlift photobioreactor

In photobioreactors, which are usually operated under light limitation,sufficient dissolved inorganic carbon must be provided to avoid carbonlimitation. Efficient mass transfer of CO₂ into the culture mediumisdesirable since undissolved CO₂ is lost by outgassing. Mass transferof O₂ out of the system is also an important consideration, due tothe need to remove photosynthetically-derived O₂ before it reachesinhibitory concentrations. Hydrodynamics (mixing characteristics) are afunctionof reactor geometry and operating conditions (e.g. gas and liquid flow rates),and are a principal determinant of the light regime experienced by the culture.This in turn affects photosynthetic efficiency, productivity, and cellcomposition. This paper describes the mass transfer and hydrodynamics within anear-horizontal tubular photobioreactor. The volume, shape and velocity ofbubbles, gas hold-up, liquid velocity, slip velocity, axial dispersion,Reynoldsnumber, mixing time, and mass transfer coefficients were determined intapwater,seawater, and algal culture medium. Gas hold-up values resembled those ofvertical bubble columns, and the hydraulic regime could be characterized asplug-flow with medium dispersion. The maximum oxygen mass transfer coefficientis approximately 7 h^–1. A regime analysisindicated that there are mass transfer limitations in this type ofphotobioreactor. A methodology is described to determine the mass transfercoefficients for O₂ stripping and CO₂ dissolution whichwould be required to achieve a desired biomass productivity. This procedure canassist in determining design modifications to achieve the desired mass transfercoefficient.     

Experimental and theoretical assessment of maximum productivities for the microalgae Chlamydomonas reinhardtii in two different geometries of photobioreactors

The validity of a simple, reliable, and useful recently published formula enabling to calculate the maximum volumetric biomass productivities in photobioreactors (PBRs) was investigated through the cultivation of the microalga Chlamydomonas reinhardtii. Experimental maximum kinetic performances accurately obtained in two different, artificially lightened torus‐plane and cylindrical reactors having the same specific illuminated area confirmed the availability, power, and robustness of such formula. The predictive kinetic parameters previously proposed and validated with cyanobacteria were then proved general and robust in case of eukaryotic microalgae, as postulated in the founding article. In this case, an additional criterion requiring rigorous control of the working illuminated fraction γ = 1 ± (15%) inside the reactor is demonstrated. For this, the usefulness and reliability of a generalized two‐flux model accurately describing the radiation field inside turbid culture media of C. reinhardtii were also established in this article. These important results contribute to identify the main engineering factors governing light‐limited PBRs functioning and then to clarify some misinterpretations widely reported in the literature. Together with the referenced previous work, this article gives a framework toward optimal conception of PBRs on a strong physical basis. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

A model for light distribution and average solar irradiance inside outdoor tubular photobioreactors for the microalgal mass culture

A mathematical model to estimate the solar irradiance profile and average light intensity inside a tubular photobioreactor under outdoor conditions is proposed, requiring only geographic, geometric, and solar position parameters. First, the length of the path into the culture traveled by any direct or disperse ray of light was calculated as the function of three variables: day of year, solar hour, and geographic latitude. Then, the phenomenon of light attenuation by biomass was studied considering Lambert-Beer's law (only considering absorption) and the monodimensional model of Cornet et al. (1900) (considering absorption and scattering phenomena). Due to the existence of differential wavelength absorption, none of the literature models are useful for explaining light attenuation by the biomass. Therefore, an empirical hyperbolic expression is proposed. The equations to calculate light path length were substituted in the proposed hyperbolic expression, reproducing light intensity data obtained in the center of the loop tubes. The proposed model was also likely to estimate the irradiance accurately at any point inside the culture. Calculation of the local intensity was thus extended to the full culture volume in order to obtain the average irradiance, showing how the higher biomass productivities in a Phaeodactylum tricornutum UTEX 640 outdoor chemostat culture could be maintained by delaying light limitation. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 701-714, 1997.     

Production of eicosapentaenoic acid by Nannochloropsis sp. cultures in outdoor tubular photobioreactors

Autotrophic microalgae cultures have been proposed as an alternative source of EPA, a nutritionally important polyunsaturated fatty acid that plays a key role in the prevention and treatment of several human diseases and disorders. The technology currently available is however, considered commercially not viable because of the low degree of control of algae cultures in outdoor open ponds. The use of closed reactors could overcome these limitations and bring EPA production by microalgae closer to becoming a reality. In this study, we have demonstrated the feasibility of outdoor cultivation of Nannochloropsis sp. in tubular reactors and the potential of this eustigmatophyte as an alternative source of EPA. Nannochloropsis sp. was cultivated in NHTRs of different sizes (from 10.2 to 610 l) from spring to autumn under the climatic conditions of central Italy. EPA productivity essentially reflected the productivity of the culture and reached its maximum in May–June (mean monthly value: 32 mg l⁻¹ day⁻¹). Although the fatty acid composition of the biomass varied significantly during the cultivation period, EPA content remained rather stable around the value of 4% of dry biomass. The transfer of the cultures from laboratory to outdoor conditions, the exposure to natural light–dark cycles, along with lowering the salt concentration from 33 g l⁻¹ (seawater salinity value) to 20 g l⁻¹, factors that caused lasting modifications in the fatty acid content and composition of Nannochloropsis sp., did not significantly affect the EPA content of the biomass.     

Hydrodynamics and mass transfer of CO2 in water in a tubular photobioreactor

Microalgae cultivation has received growing importance because of its potential applications in CO₂ bio‐fixation, wastewater treatment and biofuel production. In this regard, proper design of photobioreactors is crucial for large‐scale commercial applications. The hydrodynamics of a photobioreactor has great influence on the transfer of CO₂ from gas phase to liquid phase. Considering the facts, the present research focused on studying the gas holdups and mass transfer from the gas to liquid phase in a tubular photobioreactor at various superficial liquid velocities ranging from 8.4 to 22.4 cm/s and superficial gas velocities ranging from 3.66 to 8.1 cm/s. It was found that the gas holdups were radially distributed. The highest gas holdups were observed at the center zone while the lowest holdups are found near the reactor wall. CO₂ mass transfer coefficient in the photobioreactor was also estimated under different superficial liquid velocities (0.206, 0.355 and 0.485 cm/s) and gas velocities (0.67, 1.16 and 1.37 cm/s). The overall mass transfer coefficient was estimated by fitting the experimental data and comparing results with an unsteady state differential mole balance equation solved by Runge‐Kutta‐Gill method. Model predictions were comparable to experimental results.     

An integrated solar and artificial light system for internal illumination of photobioreactors

Exploitation of photosynthetic cells for the production of useful metabolites requires efficient photobioreactors. Many laboratory scale photobioreactors have been reported but most of them are extremely difficult to scale up. Furthermore, the use of open ponds and outdoor tubular photobioreactors is limited by the requirement for large spaces and the difficulty in maintaining sterile conditions. In view of this, we have designed and constructed an internally illuminated stirred tank photobioreactor. The photobioreactor is simple, heat sterilizable and mechanically agitated like the conventional stirred tank bioreactors. Furthermore, it can easily be scaled up while maintaining the light supply coefficient and thus the productivity constant. A device was installed for collecting solar light and distributing it inside the reactor through optical fibers. It was equipped with a light tracking sensor so that the lenses rotate with the position of the sun. This makes it possible to use solar light for photosynthetic cell cultivation in indoor photobioreactors. As a solution to the problems of night biomass loss and low productivity on cloudy days, an artificial light source was coupled with the solar light collecting device. A light intensity sensor monitors the solar light intensity and the artificial light is automatically switched on or off, depending on the solar light intensity. In this way, continuous light supply to the reactor is achieved by using solar light during sunny period, and artificial light at night and on cloudy days.     

Performance characteristics of electron transfer dissociation mass spectrometry

We performed a large scale study of electron transfer dissociation (ETD) performance, as compared with ion trap collision-activated dissociation (CAD), for peptides ranging from approximately 1000 to 5000 Da (n approximately 4000). These data indicate relatively little overlap in peptide identifications between the two methods ( approximately 12%). ETD outperformed CAD for all charge states greater than 2; however, regardless of precursor charge a linear decrease in percent fragmentation, as a function of increasing precursor m/z, was observed with ETD fragmentation. We postulate that several precursor cation attributes, including peptide length, charge distribution, and total mass, could be relevant players. To examine these parameters unique ETD-identified peptides were sorted by length, and the ratio of amino acid residues per precursor charge (residues/charge) was calculated. We observed excellent correlation between the ratio of residues/charge and percent fragmentation. For peptides of a given residue/charge ratio, there is no correlation between peptide mass and percent fragmentation; instead we conclude that the ratio of residues/charge is the main factor in determining a successful ETD outcome. As charge density decreases so does the probability of non-covalent interactions that can bind a newly formed c/z-type ion pair. Recently we have described a supplemental activation approach (ETcaD) to convert these non-dissociative electron transfer product ions to useful c- and z-type ions. Automated implementation of such methods should remove this apparent precursor m/z ceiling. Finally, we evaluated the role of ion density (both anionic and cationic) and reaction duration for an ETD experiment. These data indicate that the best performance is achieved when the ion trap is filled to its space charge limit with anionic reagents. In this largest scale study of ETD to date, ETD continues to show great promise to propel the field of proteomics and, for small- to medium-sized peptides, is highly complementary to ion trap CAD.     

Determination of external and internal mass transfer limitation in nitrifying microbial aggregates

In this article we present a study of the effects of external and internal mass transfer limitation of oxygen in a nitrifying system. The oxygen uptake rates (OUR) were measured on both a macro-scale with a respirometric reactor using off-gas analysis (Titrimetric and Off-Gas Analysis (TOGA) sensor) and on a micro-scale with microsensors. These two methods provide independent, accurate measurements of the reaction rates and concentration profiles around and in the granules. The TOGA sensor and microsensor measurements showed a significant external mass transfer effect at low dissolved oxygen (DO) concentrations in the bulk liquid while it was insignificant at higher DO concentrations. The oxygen distribution with anaerobic or anoxic conditions in the center clearly shows major mass transfer limitation in the aggregate interior. The large drop in DO concentration of 22-80% between the bulk liquid and aggregate surface demonstrates that the external mass transfer resistance is also highly important. The maximum OUR even for floccular biomass was only attained at much higher DO concentrations (approximately 8 mg/L) than typically used in such systems. For granules, the DO required for maximal activity was estimated to be >20 mg/L, clearly indicating the effects of the major external and internal mass transfer limitations on the overall biomass activity. Smaller aggregates had a larger volumetric OUR indicating that the granules may have a lower activity in the interior part of the aggregate.     

Comparative analysis of the outdoor culture of Haematococcus pluvialis in tubular and bubble column photobioreactors

The present paper makes a comparative analysis of the outdoor culture of H. pluvialis in a tubular photobioreactor and a bubble column. Both reactors had the same volume and were operated in the same way, thus allowing the influence of the reactor design to be analyzed. Due to the large changes in cell morphology and biochemical composition of H. pluvialis during outdoor culture, a new, faster methodology has been developed for their evaluation. Characterisation of the cultures is carried out on a macroscopic scale using a colorimetric method that allows the simultaneous determination of biomass concentration, and the chlorophyll, carotenoid and astaxanthin content of the biomass. On the microscopic scale, a method was developed based on the computer analysis of digital microscopic images. This method allows the quantification of cell population, average cell size and population homogeneity. The accuracy of the methods was verified during the operation of outdoor photobioreactors on a pilot plant scale. Data from the reactors showed tubular reactors to be more suitable for the production of H. pluvialis biomass and/or astaxanthin, due to their higher light availability. In the tubular photobioreactor biomass concentrations of 7.0 g/L (d.wt.) were reached after 16 days, with an overall biomass productivity of 0.41 g/L day. In the bubble column photobioreactor, on the other hand, the maximum biomass concentration reached was 1.4 g/L, with an overall biomass productivity of 0.06 g/L day. The maximum daily biomass productivity, 0.55 g/L day, was reached in the tubular photobioreactor for an average irradiance inside the culture of 130 microE/m2s. In addition, the carotenoid content of biomass from tubular photobioreactor increased up to 2.0%d.wt., whereas that of the biomass from the bubble column remained roughly constant at values of 0.5%d.wt. It should be noted that in the tubular photobioreactor under conditions of nitrate saturation, there was an accumulation of carotenoids due to the high irradiance in this reactor, their content in the biomass increasing from 0.5 to 1.0%d.wt. However, carotenoid accumulation mainly took place when nitrate concentration in the medium was below 5.0mM, conditions which were only observed in the tubular photobioreactor. A similar behaviour was observed for astaxanthin, with maximum values of 1.1 and 0.2%d.wt. measured in the tubular and bubble column photobioreactors, respectively. From these data astaxanthin productivities of 4.4 and 0.12 mg/L day were calculated for the tubular and the bubble column photobioreactors. Accumulation of carotenoids was also accompanied by an increase in cell size from 20 to 35 microm, which was only observed in the tubular photobioreactors. Thus it may be concluded that the methodology developed in the present study allows the monitoring of H. pluvialis cultures characterized by fast variations of cell morphology and biochemical composition, especially in outdoor conditions, and that tubular photobioreactors are preferable to bubble columns for the production of biomass and/or astaxanthin.     

Heat and mass transfer effects in static solid-substrate fermentations: design of fermentation chambers

An experimental device was constructed to allow nearly simultaneous measurements to be made on temperature and gas composition at different depths in a solid-substrate fermentation bed. The time-dependent values of temperature, mol % O(2) and mol % CO(2) were measured at five positions in beds 6.35 cm (2.5 in.) deep. With a tempeh fermentation (Rhiopus oligosporus growing on soybeans) the temperature gradient could be as steep as 3 degrees C/cm during active mold growth and concentration of CO(2) could reach 21 vol. % in the bottom layer.     

Light/dark cyclic movement of algal culture (<Emphasis Type="Italic">Synechocystis aquatilis</Emphasis>) in outdoor inclined tubular photobioreactor equipped with static mixers for efficient production of biomass

Synechocystis aquatilis SI-2 was grown outdoors in a 12.5cm diam. tubular photobioreactor equipped with static mixers. The static mixers ensured that cells were efficiently circulated between the upper (illuminated) and lower (dark) sections of the tubes. The biomass productivity varied from 22 to 45g m^–2d^–1, with an average of 35g m^–2d^–1, etc which corresponded to average CO₂ fixation rate of about 57 g CO₂ m^–2 d^–1. The static mixers not only helped in improving the biomass productivities but also have a high potential to lower the photoinhibitory effect of light during the outdoor cultures of algae. Revisions requested 27 July 2004; Revisions received 12 November 2004     

Prediction of dissolved oxygen and carbon dioxide concentration profiles in tubular photobioreactors for microalgal culture

A model is developed for prediction of axial concentration profiles of dissolved oxygen and carbon dioxide in tubular photobioreactors used for culturing microalgae. Experimental data are used to verify the model for continuous outdoor culture of Porphyridium cruentum grown in a 200-L reactor with 100-m long tubular solar receiver. The culture was carried out at a dilution rate of 0.05 h-1 applied only during a 10-h daylight period. The quasi-steady state biomass concentration achieved was 3.0 g. L-1, corresponding to a biomass productivity of 1.5 g. L-1. d-1. The model could predict the dissolved oxygen level in both gas disengagement zone of the reactor and at the end of the loop, the exhaust gas composition, the amount of carbon dioxide injected, and the pH of the culture at each hour. In predicting the various parameters, the model took into account the length of the solar receiver tube, the rate of photosynthesis, the velocity of flow, the degree of mixing, and gas-liquid mass transfer. Because the model simulated the system behavior as a function of tube length and operational variables (superficial gas velocity in the riser, composition of carbon dioxide in the gas injected in the solar receiver and its injection rate), it could potentially be applied to rational design and scale-up of photobioreactors. Copyright 1999 John Wiley & Sons, Inc.