Continuous Production of Lipids with Microchloropsis salina in Open Thin-Layer Cascade Photobioreactors on a Pilot Scale

: Studies on microalgal lipid production as a sustainable feedstock for biofuels and chemicals are scarce, particularly those on applying open thin-layer cascade (TLC) photobioreactors under dynamic diurnal conditions. Continuous lipid production with Microchloropsis salina was studied in scalable TLC photobioreactors at 50 m 2 pilot scale, applying a physically simulated Mediterranean summer climate. A cascade of two serially connected TLC reactors was applied, promoting biomass growth under nutrient-replete conditions in the ﬁrst reactor, while inducing the accumulation of lipids via nitrogen limitation in the second reactor. Up to 4.1 g L − 1 of lipids were continuously produced at productivities of up to 0.27 g L − 1 d − 1 (1.8 g m 2 d − 1 ) at a mean hydraulic residence time of 2.5 d in the ﬁrst reactor and 20 d in the second reactor. Coupling mass balances with the kinetics of microalgal growth and lipid formation enabled the simulation of phototrophic process performances of M. salina in TLC reactors in batch and continuous operation at the climate conditions studied. This study demonstrates the scalability of continuous microalgal lipid production in TLC reactors with M. salina and provides a TLC reactor model for the realistic simulation of microalgae lipid production processes after re-identiﬁcation of the model parameters if other microalgae and/or varying climate conditions are applied.


Introduction
In the face of a growing world population and the associated increase of energy and food demand, microalgal biomass is considered a promising, renewable feedstock for a sustainable bioeconomy. With the ability to harvest light energy while recirculating carbon dioxide from air or flue gases, as well as removing nitrogen and phosphorus from municipal or agricultural wastewater [1,2], the utilization of biomass from microalgae can contribute to several of the United Nation's Sustainable Development Goals, e.g., affordable and clean energy, climate action, responsible consumption and production, and zero hunger [3]. Major advantages of microalgae over terrestrial crop plants are the approximate 10 times higher productivities with shorter growth cycles and less consumption of fresh water [4,5]. Additionally, they can be cultivated on non-fertile ground, thereby avoiding the competition for agricultural land. Although land-based mobility is expected to use more and more electrical energy, electrical or hydrogen-based propulsion is not expected to scale up or comply with safety regulations for aviation and shipping in the near future [6]. To swiftly support CO 2 emission reductions in these sectors, and needing a high energy density, the utilization of synthetic or biofuels might offer a drop-in solution [7]. However, despite much effort to establish microalgal biomass as a sustainable feedstock for bioenergy for more than 40 years, economically feasible processes are scarce and have only been developed for a few high-value products like nutraceuticals, pigments, or other specialty chemicals [8,9]. Development and commercialization of microalgae processes are mainly limited by the high costs of algal biomass production compared to conventional crops [10,11]. High operating costs are caused (i) by the power input, which is necessary for circulating the diluted microalgal suspension in the photobioreactors at low growth rates, resulting in long process times and (ii) by the separation of huge amounts of water during cell harvest [12]. The overall costs are further increased by high capital costs for large-scale production facilities at often remote locations with suitable climate conditions.
Because operational and capital costs of closed photobioreactors are especially high, only open photobioreactors, meaning photobioreactors with open surfaces to the atmosphere, are considered for a feasible production of microalgal biomass [13]. In this respect, open raceway ponds are the most commonly applied photobioreactors for producing microalgal biomass. However, raceway ponds are limited to very dilute microalgal suspensions of only 0.3-1.0 g L −1 cell dry weight (CDW) because of low mixing and mutual shading of algae cells in the long light path through the fluid layer of up to 30 cm [14,15]. An open photobioreactor system designed to overcome this limitation is the thin-layer cascade (TLC) reactor. Here, the culture gravimetrically flows along a sloped channel in a thin fluid layer of <1 cm, thereby increasing both flow turbulence and the surface-tovolume ratio, resulting in a much higher volumetric productivity of the algal culture and lower costs for water removal [16]. Turbulent flow increases light-dark cycle frequency to prevent excessive photoinhibition on the suspension surface as well as light limitation on the light-averted side. Thus, up to 50 g L −1 CDW can be achieved with TLC reactors in nutrient-replete batch processes, which was shown with Chlorella sp. and Microchloropsis salina (formerly Nannochloropsis salina) [17,18]. Additionally, high microalgal biomass concentrations decrease the culture's susceptibility to invading organisms, a common problem in open pond systems [19,20].
While suitable microalgae strains grow rapidly under optimal environmental conditions, some species are also able to accumulate high amounts of lipids, mainly triacylglycerides, if physiological stress factors are applied, making them a promising feedstock for biofuel production [21]. The most widely studied stress factor to induce the accumulation of lipids in microalgae is nitrogen limitation [22]. If an insufficient nitrogen supply limits protein synthesis, photosynthetically fixated carbon and electrons are diverted to lipid synthesis instead, to mitigate an imbalance of redox equivalents and oxidative damage [23,24]. In this way, the batch production of up to 6.6 g L −1 of lipids was recently reported with a maximum lipid quota of 46% (w/w) with M. salina, cultivated indoors with artificial seawater with a physically reproduced Mediterranean summer climate, applying a TLC reactor with a surface area of 8 m 2 [25]. This two-phase batch process, consisting of a nutrient-replete growth phase followed by a nitrogen-limited lipid accumulation phase, was transferred to a continuously operated cascade of two serially connected TLC reactors. Here, the first TLC photobioreactor was continuously supplied with fresh cultivation medium to promote rapid growth, while lipid accumulation was induced in the second TLC reactor under nutrient-limited conditions. Thereby, continuous production of 3.0-3.5 g L −1 lipids was observed with M. salina at a productivity of 0.2 g L −1 d −1 (1.35 g m −2 d −1 ) lipids within 24 d of continuous operation [25].
So far, microalgal lipid production has mostly been studied at laboratory scale or in well-controlled but expensive closed photobioreactors. However, data on large-scale processes in open reactors under outdoor climate conditions is necessary to bridge the gap to a commercial, large-scale production of microalgae biomass. In this respect, experimental efforts for process development can be reduced by computational simulations, applying validated models for algal growth and lipid formation. In this study, we report on the continuous production of lipid-rich M. salina biomass in a scalable 50 m 2 TLC photobioreactor under a physically simulated Mediterranean summer climate. Open TLC reactors were operated with artificial seawater in the TUM-AlgaeTec Center (Technical University of Munich, Taufkirchen, Germany), a research facility designed for the indoor evaluation of photoautotrophic microalgae processes under a realistic reproduction of outdoor sun-Energies 2021, 14, 500 3 of 20 light intensity, temperature, and air humidity with dynamic diurnal cycles. Additionally, a mathematical model was developed and validated, coupling reactor mass balances with microalgae reaction kinetics to simulate M. salina growth and lipid production under dynamic light conditions in TLC photobioreactors in batch or continuous mode.

Climate Simulation
All experiments were conducted at the TUM-AlgaeTec Center, a facility for indoor pilot-scale microalgae processes under realistically reproduced outdoor light and air conditions. TLC photobioreactors were located inside glass halls and illuminated by natural sunlight. LED-panels emitting artificial sunlight (FutureLED, Berlin, Germany) supplemented the local irradiance in the 400 to 750 nm range according to a set target irradiance. Automatically controlled windows as well as an air-conditioning system controlled the air temperature inside the glass halls. Irradiance and air temperature were reproduced daily according to the climate data of 15 June 2012 in Almería, Spain, a sunny day with a 14:10 light-dark cycle and a temperature range of 17-30 • C. The maximum light intensity in the photosynthetically active radiation (PAR) range (400-700 nm) was 1823 µmol m −2 s −1 . A detailed description of the TUM-AlgaeTec Center and climate simulation has previously been given [17].

Thin-Layer Cascade Photobioreactor Operation
Two types of open TLC photobioreactors with an illuminated surface area of 8 m 2 and 50 m 2 were used in this study. 8 m 2 reactors with a working volume of 55 L consisted of an upper and a lower 4 m × 1 m channel made of polyethylene with an inclination of 1 • each in opposite direction, connected by a flow reversal module. A magnetically coupled centrifugal pump (MKPG, Ventaix, Monschau, Germany) with a 90 mm polypropylene rotor circulated the culture suspension at 2.4 L s −1 day and night from a retention tank at the end of the lower channel back to an inlet module at the start of the upper channel. This flow rate was chosen as a good compromise between turbulent mixing and energy saving considerations since it ensures a flow regime in the transition range at a Reynolds number of 2347 [17,27]. About 500 mL of tap water were automatically added via a magnetic valve as soon as a binary level-sensor (LFFS, Baumer, Friedberg, Germany) in the retention tank detected a loss of volume due to evaporation. During the day, pH was controlled at pH 8.5 by the addition of pure CO 2 via a mass flow controller (red-y smart, Vögtlin, Aesch, Switzerland) through perforated hoses (Solvox B, Linde, Pullach, Germany) with a total surface area of 226 cm 2 installed at the bottom of the retention tank. A detailed description of design, construction, and computational fluid dynamics simulations of the 8 m 2 TLC photobioreactor was published previously [17,28].
The pilot-scale 50 m 2 TLC bioreactor consisted of two 12 m × 2 m channels made of white woven coated polyethylene pond liner (areal weight 320 g m −2 , Daedler, Trittau, Germany). As with the 8 m 2 TLC reactor, both channels were inclined 1 • in opposite directions; however, they were installed at the same height and connected on both sides via an open retention tank, centrifugal pump, and inlet module, instead of using a flow reversal module on one side. This change allows for better scaling of the reaction system, since multiple channels can be connected in parallel on inclined ground-level ramps; however, at the cost of additional pumping stations. Target flow rate of both centrifugal pumps was set to 4.8 L s −1 in order to maintain identical hydrodynamic conditions (2.4 L s −1 m −1 in relation to channel width) in the 8 m 2 and 50 m 2 photobioreactors, respectively. The same CO 2 gassing hoses and level sensors as used before were installed in both retention tanks, while pH measurement and automatic addition of tap water were exclusive to one tank. Since the actual reactor volume depends on the fluid level in both retention tanks, tap water addition occurred only when both level sensors registered a reduced volume simultaneously for at least 12 s. The level sensors additionally served to modulate the volume flow of each respective pump in an interval of ±0.15 L s −1 to level out both tanks and ensure uniform distribution of the microalgal suspension in the entire photobioreactor. The main characteristics of both TLC reactor designs are summarized in Table 1. A photograph of the 50 m 2 TLC photobioreactor is shown in Figure 1.
8 m 2 TLC reactors were inoculated with M. salina to achieve an initial concentration of 0.3 g L −1 CDW with microalgal cells from a 4 m 2 pre-culture TLC reactor. The 50 m 2 TLC reactor was inoculated to initially achieve 0.6 g L −1 CDW in order to prevent a previously observed excessive photoinhibition in the beginning of the cultivation, which might have been the result of the longer channels and higher surface-to-volume ratio in the dilute culture at pilot scale [29]. For continuous lipid production, the second 50 m 2 TLC photobioreactor, initially supplied with ASW plus 1× concentrated feed medium to induce the accumulation of lipids at the end of the preliminary batch phase, was used in series. Continuous operation was initiated at the same time as the first 8 m 2 TLC reactor, using the harvest stream of the first reactor as influent for the second reactor without additional nutrient supply. Since the accumulation of lipids under nitrogen-limited conditions in the second reactor is a much slower process than microalgal growth under nutrient-replete conditions in the first reactor, the dilution rate of the second TLC reactor was set to 0.05 d −1 while the first TLC reactor was operated at 0.4 d −1 . These different dilution rates allowed using a 50 m 2 reactor, supplied by an 8 m 2 reactor for biomass production, for lipid accumulation. To achieve this difference in dilution rates between the TLC photobioreactors in series, 25% of the harvest stream of the first reactor was discarded.

Optical Density and Cell Dry Weight
Cell dry weight was determined by optical density measurement at 750 nm (OD750) in triplicate with an UV-Vis spectrophotometer (Genesys 10S UV-VIS, Thermo Fisher Scientific Inc., Waltham, MA, USA). Additionally, CDW was measured gravimetrically once per day by filtration on pre-dried and weighted glass-microfiber filters (GF/C, Whatman, GE Healthcare, Chicago, IL, USA) in triplicate to obtain a linear correlation factor between

Continuous Operation of Thin-Layer Cascades
8 m 2 TLC reactors were operated continuously under the same conditions as in batch mode. The photobioreactor was initially supplied with ASW medium plus 4× concentrated feed medium to reach about 6-7 g L −1 CDW in the initial batch phase before the continuous operation was started. The reactor was continuously supplied with ASW medium plus additional 2-4× concentrated feed medium to ensure a urea concentration of 0.9-1.5 g L −1 in the microalgal suspension. Continuous medium supply and harvest via peristaltic pumps (530DuN, Watson-Marlow, Rommerskirchen, Germany) were stopped automatically between 8 p.m. and 6 a.m. to prevent wash-out of biomass at night. A constant feeding and harvest rate . V was fixed according to Equation (1) to achieve the favored constant dilution rate D during a daylight-phase of 14 h (with reactor volume V).
For continuous lipid production, the second 50 m 2 TLC photobioreactor, initially supplied with ASW plus 1× concentrated feed medium to induce the accumulation of lipids at the end of the preliminary batch phase, was used in series. Continuous operation was initiated at the same time as the first 8 m 2 TLC reactor, using the harvest stream of the first reactor as influent for the second reactor without additional nutrient supply. Since the accumulation of lipids under nitrogen-limited conditions in the second reactor is a much slower process than microalgal growth under nutrient-replete conditions in the first reactor, the dilution rate of the second TLC reactor was set to 0.05 d −1 while the first TLC reactor was operated at 0.4 d −1 . These different dilution rates allowed using a 50 m 2 reactor, supplied by an 8 m 2 reactor for biomass production, for lipid accumulation. To achieve this difference in dilution rates between the TLC photobioreactors in series, 25% of the harvest stream of the first reactor was discarded.

Optical Density and Cell Dry Weight
Cell dry weight was determined by optical density measurement at 750 nm (OD 750 ) in triplicate with an UV-Vis spectrophotometer (Genesys 10S UV-VIS, Thermo Fisher Scientific Inc., Waltham, MA, USA). Additionally, CDW was measured gravimetrically once per day by filtration on pre-dried and weighted glass-microfiber filters (GF/C, Whatman, GE Healthcare, Chicago, IL, USA) in triplicate to obtain a linear correlation factor between CDW and OD 750 for each experiment. Loaded filters were washed with deionized water and dried at 80 • C for at least 48 h before weighing. In some processes, the optical density was additionally measured online via an optical density-sensor (ALS-OD4, algae lab systems, Boulder, CO, USA) up to the detection limit of 11-12 g L −1 CDW. Online data was calibrated with manual OD 750 measurements for each process.

Total Lipid Analysis
The total lipid concentration of the algae suspension was determined via a modified sulfo-phospho-vanillin (SPV) assay in triplicates [30,31]. A 0.3 g measure of vanillin was dissolved in 5 mL absolute ethanol and 45 mL deionized water. 200 mL phosphoric acid Energies 2021, 14, 500 6 of 20 was added, yielding the phospho-vanillin reagent. A 50 µL measure of a microalgae sample was incubated for 10 min in 1 mL sulfuric acid (98%) at 90 • C. After cooling on ice for 5 min, 2.5 mL phospho-vanillin reagent was added, thoroughly mixed and incubated for 15 min at 37 • C and 900 rpm (Thermomixer basic, CellMedia, Elsteraue, Germany). The absorption was then measured at 530 nm with an UV-Vis spectrophotometer (Genesys 10S UV-VIS, Thermo Fisher Scientific Inc., Waltham, MA, USA) against a blank of water, which was treated in the same way as the algal samples. An external standard of rapeseed oil was used to linearly correlate the absorption to the total lipid concentration.

Urea and Salinity Measurement
Salinity and urea were analyzed daily in the supernatant of a centrifuged sample (14,500× g, 4 min, Espresso, Thermo Fisher, Waltham, MA, USA). The salinity was measured by a refractometer (Hanna Instruments, Vöhringen, Germany) in the ppt range. An enzymatic urea/ammonia assay (R-Biopharm AG, Darmstadt, Germany) based on the stoichiometric conversion of NADH to NAD + via urease and glutamate dehydrogenase was used according to the manufacturer's instructions to determine the urea concentration photometrically at 340 nm.

Specific Growth Rate and Biomass Productivity
In diurnal microalgal cultures, two types of specific growth rates were estimated: the daily growth rate considers multiple samples during the daylight phase of a single day, while the inter-day growth rate is based on one respective sample at a specific daytime over multiple days. Since the inter-day growth rate also includes the night phase, it is usually much slower compared to the daily growth rate. The daily specific growth rate µ during the daylight phase in exponentially growing batch processes was estimated based either on five to six manual CDW concentration measurements c X or, if available, with online OD data measured by an optical density-sensor (ALS-OD4, algae lab systems, Boulder, CO, USA), which was calibrated with manual OD 750 measurements. The daily specific growth rate µ was estimated by nonlinear regression applying the Levenberg-Marquardt algorithm with the exponential growth function, assuming ideal mixing in the TLC photobioreactor (Equation (2)).
Inter-day growth rates were estimated in the same way based on CDW concentration data at 10 a.m. over several days.
The volumetric productivity P i,n of product i (biomass or lipids) in a single TLC reactor n in continuous operation was estimated based on the sum of the product inside the reactor volume and the integral of product being harvested, assuming an ideally mixed bioreactor (Equation (3)).
with the influent and harvest volume flow . V n and the product concentration in reactor n c i,n and in the influent c in i,n . Integration was performed via the cumtrapz Matlab (Matlab R2020a, Mathworks, Natick, MA, USA) function, based on linearly interpolated data between samples.
The overall productivity of the two-stage continuous cascade considers the total amount of product harvested from the second reactor. Since the volume flow of the first TLC reactor was higher than the volume flow of the second, only the fraction of the first reactor that was necessary to supply the second was taken into account to calculate the total volume V total of the cascade (Equation (4)).
Energies 2021, 14, 500 7 of 20 with the volumes V 1 and V 2 of reactor 1 and 2. The overall biomass and lipid productivity of the two-stage cascade P i,total was then estimated by means of Equation (5) with the product concentration in the second reactor c i,2 .
2.9. Modeling 2.9.1. Kinetics of Microalgae Growth Phototrophic microalgae processes with M. salina in TLC photobioreactors were modeled by coupling reactor mass balances with kinetics of microalgae growth and lipid formation. The limiting-state variable influencing phototrophic microalgae growth is the availability of light. The incident photosynthetic photon flux density (PPFD) I 0 on the reactor surface is attenuated over the culture layer l by algal cells via absorption and scattering. At sufficiently low biomass concentrations or short light paths, the effective PPFD at layer-depth l is given by the transmission I in Lambert-Beer's law (Equation (6)): with the CDW concentration c X and the specific extinction coefficient ε. Since light availability decreases with increasing layer-depth, up to three light regimes can be found in microalgal cultures [32]: a light-limited regime at a low PPFD, where microalgal growth increases with increasing irradiance, is typically the case at the light-averted side of the photobioreactor. Here, growth can even become negative at a very low light availability when the rate of photosynthesis does not compensate the rate of respiration. A photosaturated zone is typically found in the middle of the culture layer where the PPFD is sufficiently high to achieve a maximum photosynthetic rate. At an even higher irradiance near the reactor surface, photoinhibition can occur, decreasing microalgal growth due to redox imbalances and damage to the photosystems [33].
Although strongly varying growth rates can be expected in these different light regimes, Pfaffinger et al. [34,35] recently validated the applicability of a mean integral growth rate of the microalgae suspension, corresponding to an averaged integral photon flux density, for M. salina in flat-panel and TLC photobioreactors. Despite its inability to differentiate between light absorption, scattering, and reflection, Lambert-Beer's law in combination with this averaged integral PPFD was found to be an adequate approximation to describe the mean integral growth rate up to CDW concentrations of at least 10 g L −1 in TLC reactors (l = 0.6 cm) [35] or 5 g L −1 in flat-panel reactors (l = 2 cm) [34,36]. The integral PPFD I * is given by Equation (7) [37].
with the total suspension layer-thickness L and the attenuated irradiance I as a function of CDW concentration c X and layer-depth l according to Lambert-Beer's law (Equation (6)). When microalgae are cultivated under nitrogen-limited conditions to promote the accumulation of lipids, the concentration of the nitrogen source c N needs to be taken into account as an additional growth-limiting factor. Based on the inhibition model by Pfaffinger et al. [34,35] the mean biomass specific growth rate µ of the microalgal suspension can then be described with Equation (8).
Here, µ max represents the maximum biomass specific growth rate while K S and K I represent the half-saturation and inhibition constant for light, respectively. At a mean integral PPFD of K S or K I (K S < K I ), the biomass specific growth rate is approximately half of its maximum when the nitrogen source is not limiting. The sensitivity factor ϕ is proportional to the decline of the growth rate in the photoinhibition regime. When a nitrogen limitation is considered, K N gives the half-saturation concentration for the nitrogen source.
At night, when no light is available for growth, CDW concentration declines due to respiration. However, M. salina showed a decreasing biomass decay in the dark with increasing lipid quota towards the maximum lipid quota Q L,max . This observation agrees with other investigations, describing reduced nightly biomass losses in nutrient or lightlimited late-linear growth phases [38][39][40]. The nightly biomass specific decay rate b was estimated by Equation (9) with the maximum decay rate b max at the baseline lipid quota under nutrient-replete conditions Q L,0 .
The consumption rate q N of urea as nitrogen source is connected to the specific growth rate via the yield coefficient Y XN by Equation (10).

Kinetics of Lipid Formation
The accumulation of lipids in M. salina can be induced by limitation of nitrogen. In contrast to the specific growth rate, the lipid formation rate q L is therefore inversely related to the concentration of the nitrogen source c N (Equation (11)).
Q L,max gives the maximum lipid quota at which no further lipid accumulation is observed. When the concentration of the nitrogen source is zero and no additional lipids have been accumulated yet, the lipid formation rate is maximal at q L,max .
Furthermore, a redistribution of intracellular nitrogen probably enables an additional formation of microalgal biomass in the early stage of nitrogen limitation, even when the nitrogen source in the growth medium is completely consumed [41,42]. Since the observed biomass formation exceeds the lipid formation, this biomass formation can be described as the sum of the lipid formation rate and the formation rate of lipid-free biomass. However, lipid-free biomass growth leads to a decrease of the intracellular nitrogen quota Q N since no additional nitrogen is available for uptake. Lipid-free biomass growth with the specific rate µ X−L therefore only occurs above a minimum intracellular nitrogen quota Q N,min (Equation (12)).
Analogous to lipid formation, this lipid-free biomass formation rate is defined to be at the maximum at µ X−L,max when no nitrogen source is present in the growth medium, but the intracellular nitrogen quota is still high. The lipid-free biomass formation rate then declines with a decreasing nitrogen quota. The response to the nitrogen concentration in the growth medium is additionally modulated by the sensitivity factor α. The nitrogen quota Q N can be estimated via the amount of consumed nitrogen source ∆c N with nitrogen content ε N and the produced lipid-free biomass ∆c X−L (Equation (13)).

Simulation of Microalgal Growth and Lipid Formation
Since the TLC photobioreactor has a mixing time on a timescale of minutes to achieve 99% homogeneity, it can be assumed to be ideally mixed with respect to microalgal growth, which takes place on a timescale of hours [43]. Therefore, the general mass balance of component i with concentration c i in an ideally mixed reactor at identical inlet and outlet volume flows is given by Equation (13) with time t, the dilution rate D = .
V·V −1 , the concentration i in the inlet flow c in i , and the volumetric reaction rate r i of component i.
Making use of Equations (8)-(12), the volumetric reaction rates for microalgal biomass formation or decay during the day r X,day and at night r X,night , the volumetric urea consumption rate r N , and the volumetric lipid formation rate r L can be estimated with Equations (15)- (18).
Therein, c X−L = c X − c L is defined as the lipid-free biomass, considering that new lipids are synthesized by metabolically active biomass and not by already-synthesized storage compounds.
To simulate the CDW concentration, urea concentration, and lipid concentration in a TLC photobioreactor under dynamic diurnal light conditions, the respective differential equations were solved with the built-in ode45 solver of Matlab with a maximum stepsize of 0.01 d, taking into account the same irradiance data that was used for the climate simulation experiments (see Section 2.1). A continuous cascade of two serially connected reactors was simulated by defining the respective concentrations in the first TLC reactor as the inlet concentrations of the second. The model was validated by comparing simulations to a set of experiments that were not used for the identification of model parameters.
The validation experiments covered a nutrient-replete batch process, a nitrogen-limited batch process with initially supplied ASW plus 3× feed medium but no further nutrient supplementation, and a continuous cascade of two serially connected TLC reactors. The initial conditions of the simulations were set according to each respective experiment.

Identification of Model Parameters
The specific extinction coefficient ε for M. salina grown at dynamic light conditions in a TLC reactor has been determined previously [35]. Nutrient-replete batch processes with M. salina in a TLC reactor with 8 m 2 surface area under the physically simulated Mediterranean summer climate were performed to determine the light-dependent growth kinetic under dynamic diurnal light conditions ( Figure S1). To this end, the mean daily specific growth rate was plotted against the integral PPFD, based on the mean CDW concentration on the respective day. Under nutrient-replete conditions, Equation (8) can be simplified, so that Equation (18) was used for parameter identification via nonlinear regression, making use of Matlab's curve fitting toolbox, based on the experimental data of the nutrient-replete batch process (Figure 2a).
Energies 2021, 14, 500 10 of 20 a consequence of the high shear stress caused by the centrifugal pump [44,45]. However, our result is in good accordance to the average rate of nightly biomass decay of 0.17 ± 0.037 d −1 (6.8 ± 1.4% w/w) measured in three different microalgae species, including M. salina, by Edmundson and Huesemann [38] in aerated shake flasks, as well as to the rate of Athrospira platensis cultures grown in tubular outdoor reactors with an overnight loss of 5-7.6% (w/w) [46]. The same continuous process that was applied for the estimation of biomass loss at night was also used to estimate the saturation constant for urea. was calculated for the initial batch phase and the continuous phase with a urea concentration of 1.2 g L −1 in the influent medium via nonlinear regression with Equation (8), including the previously obtained kinetic parameters , , , and ( Figure 2b). The yield coefficient of 4.2 g g −1 was determined previously with urea as the nitrogen source at nutrientreplete conditions [47].
A baseline lipid quota of M. salina cells under nutrient-replete conditions of 0.15 g g −1 as well as a maximum lipid quota of 0.46 g g −1 under nitrogen-limited conditions were determined previously in a batch process with ASW plus 1× concentrated initial feed medium in a TLC reactor of 8 m 2 under physical simulation of the same Mediterranean summer climate ( Figure S3) [25]. The same process was used to estimate the maximum specific lipid-free growth rate , and the minimum intracellular nitrogen quota , .
When the nitrogen source in the growth medium is consumed completely, Equation (12) The decline of CDW concentration due to respiration in the dark was estimated as a mean biomass specific rate from 8 p.m. to 6 a.m. via online optical density measurements during the night in a continuous nutrient-replete cultivation without induction of lipid accumulation at a dilution rate of 0.3 d −1 ( Figure S2). During 14 consecutive nights, the reduction in CDW concentration amounted to 6.7 ± 2.3% per night, resulting in a maximum biomass decay rate b max of 0.17 d −1 . Nightly biomass loss might partially have been a consequence of the high shear stress caused by the centrifugal pump [44,45]. However, our result is in good accordance to the average rate of nightly biomass decay of 0.17 ± 0.037 d −1 (6.8 ± 1.4% w/w) measured in three different microalgae species, including M. salina, by Edmundson and Huesemann [38] in aerated shake flasks, as well as to the rate of Athrospira platensis cultures grown in tubular outdoor reactors with an overnight loss of 5-7.6% (w/w) [46].
The same continuous process that was applied for the estimation of biomass loss at night was also used to estimate the saturation constant K N for urea. K N was calculated for the initial batch phase and the continuous phase with a urea concentration of 1.2 g L −1 in the influent medium via nonlinear regression with Equation (8), including the previously obtained kinetic parameters µ max , K S , K I , and ϕ ( Figure 2b). The yield coefficient Y XN of 4.2 g g −1 was determined previously with urea as the nitrogen source at nutrient-replete conditions [47].
A baseline lipid quota of M. salina cells under nutrient-replete conditions of 0.15 g g −1 as well as a maximum lipid quota of 0.46 g g −1 under nitrogen-limited conditions were determined previously in a batch process with ASW plus 1× concentrated initial feed medium in a TLC reactor of 8 m 2 under physical simulation of the same Mediterranean summer climate ( Figure S3) [25]. The same process was used to estimate the maximum specific lipid-free growth rate µ X−L,max and the minimum intracellular nitrogen quota Q N,min . When the nitrogen source in the growth medium is consumed completely, Equation (12) for the specific lipid-free growth rate can be simplified to a function of only the intracellular nitrogen quota Q N (Equation (20)). µ X−L,max and Q N,min can then be estimated with experimentally measured specific lipid-free growth rates and the respective nitrogen quota via nonlinear regression of Equation (20) (Figure 3a).

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The inhibition of the lipid-free growth rate by an available nitrogen source is additionally modulated by the urea limitation sensitivity factor (Equation (12)). This model parameter could, however, not be estimated via experimental data. Since this lipid-free growth is only observed after nearly complete consumption of the nitrogen source, it follows that should be above 1 to obtain a strong inhibition of lipid-free growth at a low nitrogen concentration < . All identified model parameters are summarized in Table 2.  Urea-limitation sensitivity factor 2 - The same process data were used to estimate the maximum biomass specific lipid formation rate q L,max . Under nitrogen-depleted conditions, Equation (11) can be simplified so that q L,max can be estimated via nonlinear regression of Equation (21) to lipid formation data as a function of the lipid quota (Figure 3b).
The inhibition of the lipid-free growth rate by an available nitrogen source is additionally modulated by the urea limitation sensitivity factor α (Equation (12)). This model parameter could, however, not be estimated via experimental data. Since this lipid-free growth is only observed after nearly complete consumption of the nitrogen source, it follows that α should be above 1 to obtain a strong inhibition of lipid-free growth at a low nitrogen concentration c N < K N . All identified model parameters are summarized in Table 2. Maximum biomass specific lipid formation rate q L,max 0.08 ± 0.02 g g −1 d −1 10 c Maximum specific lipid-free growth rate µ X−L,max 0.54 ± 0.11 g g −1 d −1 11 Urea-limitation sensitivity factor

Continuous Lipid Production with Microchloropsis Salina in Thin-Layer Cascade Photobioreactors at Pilot Scale
Lipid production with M. salina was studied in a continuously operated cascade of two serially connected TLC photobioreactors under a physically simulated Mediterranean summer climate. The first reactor with a surface area of 8 m 2 was continuously supplied with fresh feed medium during the day to promote high biomass productivity. The dilution rate was constant at 0.69 d −1 from 6 a.m. to 8 p.m., resulting in an overall dilution rate of 0.40 d −1 on a 24 h basis (mean hydraulic residence time of 2.5 d). The second TLC reactor with a surface area of 50 m 2 was continuously fed from the first reactor during the day. Here, the accumulation of lipids was induced in M. salina by application of nitrogen-limited conditions due to almost complete consumption of urea used as the nitrogen source in the first TLC reactor. Since lipid accumulation in M. salina is a much slower process than biomass growth, the overall dilution rate of the second TLC reactor was set to 0.05 d −1 (mean hydraulic residence time of 20 d). This difference in dilution rates allowed the application of an 8 m 2 TLC reactor (V = 55 L) as the first open photobioreactor to supply the second 50 m 2 TLC reactor (V = 330 L).
In both reactors, continuous operation was initiated when a CDW concentration of 6-7 g L −1 was achieved after seven days of batch operation in both reactors ( Figure 4). Inter-day specific growth rates during the exponential phase in the first and second TLC photobioreactor were 0.48 ± 0.06 d −1 and 0.43 ± 0.07 d −1 , respectively. During continuous operation, the CDW concentration of the first reactor reached a steady state after 3 mean hydraulic residence times at 6.5 ± 0.3 g L −1 , resulting in a stable biomass productivity of 2.6 g L −1 d −1 (17.9 g m −2 d −1 ). The lipid quota in the first reactor remained constant at 16.5 ± 2.0% (w/w), indicating no distinct lipid accumulation due to a sufficient nutrient supply.
The CDW concentration in the second TLC reactor increased during continuous operation up to a final concentration of 13.3 ± 0.12 g L −1 after 23 days of cultivation. Steady state was not reached, since at least 60 days of continuous cultivation would have been necessary under constant influent conditions to fulfill the requirement of at least three mean hydraulic residence times. No urea was detected in the aqueous phase in the second TLC photobioreactor after day 6, resulting in the accumulation of lipids. Hence, the lipid quota of the microalgae increased during the first seven days of continuous operation and stabilized at 30.3 ± 1.3% (w/w). The lipid concentration increased from 1.1 ± 0.1 g L −1 in the first reactor with growing microalgae to a constant lipid concentration of 3.9 ± 0.1 g L −1 in the second reactor after 18 days of cultivation, resulting in an overall lipid space-time yield (STY) of 0.24-0.27 g L −1 d −1 . The lipid STY was higher in the first TLC reactor at 0.33 g L −1 d −1 due to the high dilution rate of 0.4 d −1 , however, at only about half the lipid quota in CDW compared to the second TLC reactor. This is a typical observation in microalgae cultures due to the mutual exclusiveness of rapid biomass growth under nutrient sufficient conditions and the accumulation of lipids under nitrogen-limited conditions [48][49][50]. Nevertheless, producing lipids under the effect of a nitrogen limitation is often favored for biofuel production due to the additional benefit of shifting the lipid profile from polar functional lipids to apolar triacylglycerides with an increased saturation of fatty acids [23,51]. Additionally, nitrogen limitation reduces the protein content of the biomass [25], thereby decreasing the demand of heteroatom removal to prevent poisoning of catalysts during hydroprocessing of the bio-oil [52,53]. Energies 2021, 14, x FOR PEER REVIEW 13 of 20 Hence, continuous lipid production was successfully scaled to the 50 m 2 scale and even surpassed the previously reported lipid concentration at the 8 m 2 scale by 33% and areal productivity by 20%, respectively [25]. Furthermore, this open 50 m 2 TLC photobioreactor can be scaled easily to any size by adding additional flow channels connected via Hence, continuous lipid production was successfully scaled to the 50 m 2 scale and even surpassed the previously reported lipid concentration at the 8 m 2 scale by 33% and areal productivity by 20%, respectively [25]. Furthermore, this open 50 m 2 TLC photobioreactor can be scaled easily to any size by adding additional flow channels connected via pumping stations. To the best of our knowledge, these are the highest reported lipid concentrations (3.9 ± 0.1 g L −1 ) and overall STYs (0.24-0.27 g L −1 d −1 ) in continuously operated open microalgae processes so far. Other studies conducted under outdoor climate conditions reported lipid productivities of 0.03 g L −1 d −1 and 0.11 g L −1 d −1 with Microchloropsis gaditana in a continuously operated raceway pond and tubular photobioreactor, respectively [54,55], whereas a lipid productivity of up to 0.05 g L −1 d −1 was reported with Staurosira sp. in a 60 m 3 raceway pond in repeated batch mode [56]. A lipid concentration of 1.7 g L −1 and maximum lipid content of 31% (w/w) were achieved with Chlorella vulgaris under nitrogen-limited conditions in a 150 L TLC operated in a greenhouse [48]. A daily lipid productivity of about 0.3 g L −1 d −1 was reached in the same study, however, only for a duration of 3 days, resulting in an overall lipid productivity of about 0.2 g L −1 d −1 .

Batch Processes Applying TLC Photobioreactors
A nutrient-replete batch process was performed with M. salina, applying TLC photobioreactor with a surface area of 8 m 2 under physically simulated climate conditions. Experimental data of CDW and lipid concentration were compared to the respective simulation in order to validate model predictions (Figure 5a). The specific growth rate during the exponential growth phase did not differ significantly based on 95% confidence intervals between experiment and simulation at 0.58 ± 0.06 d −1 and 0.57 ± 0.10 d −1 , respectively. After 10 days of cultivation, the predicted CDW concentration of 23.9 g L −1 deviated only slightly (0.8%) from the experimentally measured CDW concentration of 24.1 ± 0.08 g L −1 . After 14 days of operation, the simulated (36.1 g L −1 ) surpassed the experimentally measured CDW concentration (32.2 ± 0.00 g L −1 ) with a deviation of 12.1%. The predicted lipid concentration of 3.4 g L −1 after 10 days was overestimated by 3.3% compared to the experimentally measured lipid concentration of 3.3 ± 0.07 g L −1 . As already observed with respect to cell densities, the overestimation of lipid concentration increased in the last days of the experiment. After 14 days, 4.5 ± 0.11 g L −1 and 5.6 g L −1 lipids were achieved in the experiment and simulation, respectively, resulting in a deviation of 23.8%. The average deviations of CDW and lipid concentrations between simulation and experiment over the 14-day process were 9.4 ± 4.9% and 9.9 ± 8.7%, respectively.
A second batch process applying an 8 m 2 TLC photobioreactor under the same climate conditions was performed to validate the prediction of biomass growth, lipid formation, and urea consumption with M. salina under nitrogen-limited conditions. Therefore, ASW medium with 3× additional feed medium according to an initial overall urea concentration of 1.2 g L −1 was used, without further nutrient replenishments to induce lipid accumulation after urea was completely consumed. The cultivation was terminated when CDW and lipid concentration seemed to be stationary after 34 days. During the whole process, the CDW concentration differed only slightly between experiment and simulation, reaching 15.4 ± 0.04 g L −1 and 16.1 g L −1 , respectively, with a deviation of 4.6% at the end of the process. The simulated lipid concentration after 34 days of 6.8 g L −1 resulted in a slight overestimation of 3.0% with regard to the experimental lipid concentration of 6.6 ± 0.06 g L −1 . Average deviations of CDW and lipid concentrations between simulation and experiment over the 34 days process were 8.7 ± 9.8%, and 14.1 ± 10.5%, respectively. The simulation of the urea concentration was accurate during the first 4 days of the process, declining from 1.2 g L −1 to 0.6 g L −1 . Thereafter, the urea consumption was somewhat overestimated, so that urea was completely consumed on the sixth day of the simulation, while lasting until the end of the seventh day in the experiment. imental data of 9%-14%. However, an overestimation of growth at very high CDW concentrations > 30 g L −1 suggests additional growth limiting factors at high cell densities, possibly due to an accumulation of cell debris and pigments released via cell lysis [47].

Continuous Processes Applying TLC Photobioreactors
To validate the identified growth and lipid production model of M. salina in continuous operation, a cascade of two serially connected TLC photobioreactors (8 m 2 and 50 m 2 , Section 3.1) was simulated. In this case, the predicted concentrations in the first TLC reactor were used as influent concentrations for the second reactor. In accordance with the experiment, simulation of the continuous operation was initiated on day 7 with a dilution rate of 0.4 d −1 in the first reactor and 0.05 d −1 in the second reactor. At the end of the batch phase, experimental CDW concentrations measured in the first TLC reactor of 7.1 ± 0.02 g L −1 were identical within the estimation error compared to the simulation ( Figure  6a). In the second TLC reactor, a CDW concentration of 6.9 ± 0.02 g L −1 was measured, whereas the simulation predicted 5.9 g L −1 . During continuous operation, the CDW concentration in the first reactor stabilized at a steady-state concentration of 6.5 ± 0.32 g L −1 , which was overestimated by 4.6% in the simulation at 6.8 ± 0.10 g L −1 . However, the simulation predicted a slightly smaller deviation of 0.3 g L −1 between the lowest CDW concentrations in the morning and highest in the evening compared to a difference of about 0.7 g L −1 measured experimentally. Due to a further increase in CDW concentration in nitrogen-limited conditions, the second reactor reached a maximum CDW concentration of 13.3 ± 0.12 g L −1 at the end of the process after 23 days. The simulation underestimated the final CDW concentration by 11.7% at 11.7 g L −1 . Due to the high mean hydraulic residence time of 20 days in the second reactor, a steady state was not reached during the Overall, the simulations of both the nutrient-replete and the nitrogen-limited microalgae batch processes in TLC reactors resulted in good predictions of experimental results with average deviations of CDW and lipid concentrations between simulation and experimental data of 9%-14%. However, an overestimation of growth at very high CDW concentrations > 30 g L −1 suggests additional growth limiting factors at high cell densities, possibly due to an accumulation of cell debris and pigments released via cell lysis [47].

Continuous Processes Applying TLC Photobioreactors
To validate the identified growth and lipid production model of M. salina in continuous operation, a cascade of two serially connected TLC photobioreactors (8 m 2 and 50 m 2 , Section 3.1) was simulated. In this case, the predicted concentrations in the first TLC reactor were used as influent concentrations for the second reactor. In accordance with the experiment, simulation of the continuous operation was initiated on day 7 with a dilution rate of 0.4 d −1 in the first reactor and 0.05 d −1 in the second reactor. At the end of the batch phase, experimental CDW concentrations measured in the first TLC reactor of 7.1 ± 0.02 g L −1 were identical within the estimation error compared to the simulation (Figure 6a). In the second TLC reactor, a CDW concentration of 6.9 ± 0.02 g L −1 was measured, whereas the simulation predicted 5.9 g L −1 . During continuous operation, the CDW concentration in the first reactor stabilized at a steady-state concentration of 6.5 ± 0.32 g L −1 , which was overestimated by 4.6% in the simulation at 6.8 ± 0.10 g L −1 . However, the simulation predicted a slightly smaller deviation of 0.3 g L −1 between the lowest CDW concentrations in the morning and highest in the evening compared to a difference of about 0.7 g L −1 measured experimentally. Due to a further increase in CDW concentration in nitrogen-limited conditions, the second reactor reached a maximum CDW concentration of 13.3 ± 0.12 g L −1 at the end of the process after 23 days. The simulation underestimated the final CDW concentration by 11.7% at 11.7 g L −1 . Due to the high mean hydraulic residence time of 20 days in the second reactor, a steady state was not reached during the process time. In order to reach a steady state in the second reactor, at least 3-5 mean hydraulic residence times would be necessary after achieving a steady state in the first reactor. The respective simulation of a 100-day process predicted a steady-state CDW concentration of 17.0 g L −1 .
Energies 2021, 14, x FOR PEER REVIEW 16 of 20 process time. In order to reach a steady state in the second reactor, at least 3-5 mean hydraulic residence times would be necessary after achieving a steady state in the first reactor. The respective simulation of a 100-day process predicted a steady-state CDW concentration of 17.0 g L −1 . The lipid concentration in the first TLC reactor of the experiment reached a steady state at about 1.1 ± 0.10 g L −1 after 3 mean hydraulic residence times during continuous operation. The simulation, however, resulted in an overestimation of 34.5% at a stationary lipid concentration of 1.5 g L −1 . During the last 3 days of the continuous process, the experimental data showed a decrease in lipid concentration to 0.8 ± 0.06 g L −1 , resulting in a final deviation between experiment and simulation of 87.5% after 23 days (Figure 6b). This increased deviation of the lipid concentration probably resulted from low urea concentrations near the urea saturation constant in the first reactor. is used in the model not only for biomass growth limitation (Equation (8), but also for lipid accumulation inhibition (Equation (11). The deviation between measured and predicted lipid accumulation at low urea concentrations therefore suggests that the estimation of might be flawed or an additional parameter for inhibition of the lipid accumulation might be necessary. However, the effect on lipid accumulation at a high or zero urea concentration was negligible.
In the second reactor, where urea was completely consumed, the lipid concentration increased further, reaching a maximum of 4.1 ± 0.05 g L −1 after 20 days and 3.9 ± 0.06 g L −1 at the end of the cultivation. At this process time, the simulation resulted in a 3.3% overestimated lipid concentration of 4.0 g L −1 . Since no steady state was reached during the process time of 23 days, the predicted lipid concentration further increased in a 100-day simulation to a stationary 6.6 g L −1 . The lipid concentration in the first TLC reactor of the experiment reached a steady state at about 1.1 ± 0.10 g L −1 after 3 mean hydraulic residence times during continuous operation. The simulation, however, resulted in an overestimation of 34.5% at a stationary lipid concentration of 1.5 g L −1 . During the last 3 days of the continuous process, the experimental data showed a decrease in lipid concentration to 0.8 ± 0.06 g L −1 , resulting in a final deviation between experiment and simulation of 87.5% after 23 days (Figure 6b). This increased deviation of the lipid concentration probably resulted from low urea concentrations near the urea saturation constant K N in the first reactor. K N is used in the model not only for biomass growth limitation (Equation (8), but also for lipid accumulation inhibition (Equation (11). The deviation between measured and predicted lipid accumulation at low urea concentrations therefore suggests that the estimation of K N might be flawed or an additional parameter for inhibition of the lipid accumulation might be necessary. However, the effect on lipid accumulation at a high or zero urea concentration was negligible.
In the second reactor, where urea was completely consumed, the lipid concentration increased further, reaching a maximum of 4.1 ± 0.05 g L −1 after 20 days and 3.9 ± 0.06 g L −1 at the end of the cultivation. At this process time, the simulation resulted in a 3.3% overestimated lipid concentration of 4.0 g L −1 . Since no steady state was reached during the process time of 23 days, the predicted lipid concentration further increased in a 100-day simulation to a stationary 6.6 g L −1 .
During the 23 days of cultivation, the model adequately predicted the two-stage reactor cascade for the continuous lipid production with M. salina. The average deviations of CDW concentration between simulation and experiment in the first and second reactor were 7.2 ± 6.3% and 13.5 ± 4.8%, respectively. Lipid concentration was predicted with an average deviation of 40.9 ± 27.6% and 10.2 ± 5.9% in the first and second reactor, respectively. Deviations between CDW concentrations in simulation and experiment slightly increased in the second reactor of the two-stage cascade, probably as a continuation of minor prediction errors in the first reactor. The accuracy of the simulated lipid concentration, however, increased in the second reactor due to an overestimation of lipid accumulation at urea concentrations near K N in the first reactor.
Additionally, experimental results and simulations of single-stage continuous processes with four different dilution rates at different feed concentrations in the inlet flow were compared in terms of steady state CDW concentrations after at least three mean hydraulic residence times of continuous operation (Figure 7). The dilution rates studied were 0.31 d −1 , 0.4 d −1 , 0.5 d −1 , and 0.6 d −1 , respectively with feed medium according to urea concentrations of 1.2 g L −1 , 1.5 g L −1 , 1.2 g L −1 and 0.9 g L −1 , respectively. Steadystate CDW concentrations declined at higher dilution rates of 0.5 d −1 and 0.6 d −1 in both experiments and simulations. This was expected, since the microalgal growth rate mainly depends on the availability of light in the culture suspension, which increases with decreasing CDW. The average deviation between simulation and experiment was 8.3 ± 5.0%, which further confirms the applicability of CDW simulations in continuous processes. During the 23 days of cultivation, the model adequately predicted the two-stage reactor cascade for the continuous lipid production with M. salina. The average deviations of CDW concentration between simulation and experiment in the first and second reactor were 7.2 ± 6.3% and 13.5 ± 4.8%, respectively. Lipid concentration was predicted with an average deviation of 40.9 ± 27.6% and 10.2 ± 5.9% in the first and second reactor, respectively. Deviations between CDW concentrations in simulation and experiment slightly increased in the second reactor of the two-stage cascade, probably as a continuation of minor prediction errors in the first reactor. The accuracy of the simulated lipid concentration, however, increased in the second reactor due to an overestimation of lipid accumulation at urea concentrations near in the first reactor. Additionally, experimental results and simulations of single-stage continuous processes with four different dilution rates at different feed concentrations in the inlet flow were compared in terms of steady state CDW concentrations after at least three mean hydraulic residence times of continuous operation (Figure 7). The dilution rates studied were 0.31 d −1 , 0.4 d −1 , 0.5 d −1 , and 0.6 d −1 , respectively with feed medium according to urea concentrations of 1.2 g L −1 , 1.5 g L −1 , 1.2 g L −1 and 0.9 g L −1 , respectively. Steady-state CDW concentrations declined at higher dilution rates of 0.5 d −1 and 0.6 d −1 in both experiments and simulations. This was expected, since the microalgal growth rate mainly depends on the availability of light in the culture suspension, which increases with decreasing CDW. The average deviation between simulation and experiment was 8.3 ± 5.0%, which further confirms the applicability of CDW simulations in continuous processes.
Although multiple kinetic model approaches have been published to simulate microalgal growth, some of them also including the accumulation of lipids, a large gap persists between laboratory models and their validity in large-scale outdoor production systems under real climate conditions [57,58]. In this respect, this study presents an applicable model, validated in an easily scalable open reaction system, being also the first to simulate both growth and lipid accumulation in TLC photobioreactors.   Although multiple kinetic model approaches have been published to simulate microalgal growth, some of them also including the accumulation of lipids, a large gap persists between laboratory models and their validity in large-scale outdoor production systems under real climate conditions [57,58]. In this respect, this study presents an applicable model, validated in an easily scalable open reaction system, being also the first to simulate both growth and lipid accumulation in TLC photobioreactors.