Model-Based Optimization of Microalgae Growth in a Batch Plant

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Bioengineering

Model-based optimisation of microalgae growth in a batch plant Angelo Albarello, Diana Simionato, Tomas Morosinotto, and Fabrizio Bezzo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00270 • Publication Date (Web): 14 Mar 2019 Downloaded from http://pubs.acs.org on March 20, 2019

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Industrial & Engineering Chemistry Research

Model-based optimisation of microalgae growth in a batch plant A. Albarello1, D. Simionato2, T. Morosinotto3, F. Bezzo1*

1CAPE-Lab

(Computer-Aided Process Engineering Laboratory) and PAR-Lab (Padova Algae Research

Laboratory), Department of Industrial Engineering, University of Padova, via Marzolo 9, 35131 Padova, Italy 2TMCI

Padovan SpA, via Caduti del Lavoro 7, 31029 Vittorio Veneto, Italy

3PAR-Lab

(Padova Algae Research Laboratory), Department of Biology, University of Padova, via U.

Bassi 58/B, 35131 Padova, Italy

KEYWORDS: microalgae, photobioreactor, growth model, model-based optimisation

ABSTRACT The economic sustainability of microalgae-based processes is still a major issue hindering the industrial application of such technologies. In this work, a mathematical model describing microalgae in varying light and temperature conditions is used to propose an optimised operation policy to increase productivity. The model is calibrated

ACS Paragon Plus Environment

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experimentally to describe the growth of Scenedesmus sp. cultivated in two outdoor pilot photobioreactors with different volumes, and then used to maximise algal biomass productivity by proposing a new harvesting policy of the culture. Experimental tests showed that a significant productivity increase is achievable using the optimised procedure. Simulated tests also highlighted that the additional implementation of an optimal temperature control strategy may lead to double biomass production.

1. Introduction Microalgae-based processes represent a promising alternative for the production of sustainable chemicals, particularly in the animal feed, human food, cosmetics and pharma industry1. Contributing the most to this popularity is perhaps the fact that microalgae and cyanobacteria are very plastic in modelling their photosynthetic machine and the entire metabolism in response to environmental stimuli. This plasticity depends partially on the great variety of molecules such as pigments, proteins, lipids, vitamins, produced in a species-specific manner, which have fundamental properties for algae growth and represent a panel of bioproducts that could have a strong impact on


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microalgae derived economy2; moreover, these photosynthetic microorganisms do not require agricultural land and drinkable water. However, despite their enormous potential, industrial use of microalgae is still at an early stage of development, and optimisation of design, operation and control of such photoproduction processes is yet to be investigated thoroughly, especially in the context of scaling-up the actual production capacity to increase the sustainable portfolio of microalgae-based technologies3. In practice, culture conditions at industrial scale in the so called photobioreactors (PBRs) differ drastically from the optimal conditions identified in the lab, thereby resulting in significant productivity losses. In this context, the availability of reliable mathematical models representing the key phenomena of microalgae growth could be exploited to optimise design and operation policies, and to propose advanced control strategies to bridge the gap between labscale observations and the industrial-scale reality. In fact, although most approaches to improve performance in microalgae cultivation systems are still based on experiencedriven heuristics4,5, over the last years some contributions in the scientific literature


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have demonstrated the effectiveness of model-based approaches to optimise microalgae-based processes. After the pioneering work by Sukenik et al.6, several optimisation studies were proposed in the literature. For example, He et al.7 proposed a model-based approach to optimise the flue gas utilisation in algal photobioreactors; De la Hoz Siegler et al.8 developed a model-based optimisation approach to boost biomass and microalgae oil productivities in heterotrophic cultures by acting on the culture feeding strategy; Yin-Hu et al.9 used literature models to propose optimal cultivation conditions in open ponds in terms of biomass concentration and pond depth. Grognard et al.10 developed a theoretical framework for the model-based optimisation of microalgal biomass productivity

in

photobioreactors

by acting on the dilution rate. Zhang et al.11

maximised biomass concentration in photo-mixotrophic growth by optimising dilution rate and recycle ratio in continuous reactors, and cycle time in batch reactors. Jayaraman and Rhinehart12 developed a a stochastic optimisation to increase the process profitability by acting on the harvest time and the pond depth. Malek at al.13 proposed a dynamic optimisation of dilution rate, CO2 gas flow rate, and makeup water


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flow rate in an outdoor open pond, taking into account the effect of weather conditions. De-Luca et al.14 also used weather forecasts to optimise open pond operation by dynamically controlling rates of fresh medium injection and culture removal into and from the pond. Bekirogullari et al.15 determined the optimal operating conditions for small scale batch oil production from microalgae by changing the substrate, nitrogen and inoculum initial concentrations. The literature case studies demonstrated the advantage of optimisation methods to improve process performance. However, in most literature cases only small scale lab-equipment with controlled irradiance and temperature was used to validate the model, and the actual response of microalgae growth to the optimised policy or control strategy was verified in simulated case studies or lab-scale equipment in controlled conditions. In this work a batch pilot plant for microalgae growth was used to rigorously calibrate a model of microalgal growth. The model was validated against historical data based on the current operational management of the plant and used to dynamically optimise the photobioreactor operation (i.e. the harvesting and dilution policy) to maximise productivity. Both simulations and ad-hoc experiments were then used to assess the


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proposed optimisation in a natural environment where both light and temperature fluctuate continuously. The possibility to scale-down the model to describe and optimise a smaller pilot plant was verified, too. Finally, we assessed if an optimised temperature control policy (currently not available) may help boosting productivity. Results demonstrated that even simple operations like the harvest-dilution policy, if properly optimised, may lead to significant productivity improvement, thus outperforming an operation management based on expertise and a trial and error improvement.

2. Materials and Methods Strains used in this work Scenedesmus sp. is used in this work. It has been isolated as fast growing strain starting from a pool of algae from freshwater samples from Padova, Italy. The strain was identified as Scenedesmaceae by morphological observation.

Cultivation conditions In lab scale experiments, algae are always grown in sterile BG1116 medium obtained by autoclaving at 121 °C for 15 minutes. Maintenance and propagation of cultures are performed using the same medium containing 1% agar (DuchefaBiochemie). Cells from


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solid plates are then pre-cultured in sterile BG11 liquid medium in 2 L Erlenmeyer flasks irradiated with 100 µmoles photons m-2s-1

(daylight fluorescent lamps, OSRAM

L18W/840 Cool White) measured with a LI-250A photometer (Heinz-Walz, Effeltrich, Germany). Cultures are maintained at room temperature, mixed with magnetic agitation and bubbled with atmospheric air. No external CO2 supply is provided and thus carbon dioxide to support growth derives from the atmosphere. These pre-cultures are used to inoculate the photobioreactors (PBRs) where algae are grown always using BG11 medium. Algae growing in PBRs are subjected to semi-continuous cultivation mode thus every 1, 2 or 3 days, depending on the selected trial, a specific volume of algae culture is substituted with fresh medium in order to restore a definite concentration of biomass, which is different for each set of experiments.

Analytical procedures. Algal growth was monitored daily evaluating gravimetrically biomass concentration (dry weight, DW) and optical density (OD) at 750nm exploiting a double channels spectrophotometer (CARY Series UV-VIS, Agilent Technologies). A correlation between OD750 and biomass concentration is given by the Lambert-Beer law:


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(1)

𝑂𝐷750 = 𝐾𝑎𝐶𝑏𝑙

where Cb is the biomass concentration [g/m3], Kais the extinction coefficient [m2/g] and l is the optical path [m].

Cultivation systems The cultivation system analysed in this work was designed and manufactured by TMCI Padovan SpA (Vittorio Veneto, TV, Italy) and is installed in a greenhouse located on the roof of the Department of Biology of the University of Padova, PD, Italy. The system consists of two vertical cylinders made of polymethilmethacrylate (PMMA) and stainless steel. The height of each PBR is 1 m and the diameter is 0.07 and 0.21 m resulting in 5L and 42L of working volume respectively (Figure 1). The mixing of algae cultures inside the PBR is guaranteed through the insufflation of compressed air through a nozzle located at the bottom of the cylinder. A temperature probe (JUMO Italia SRL) is located at the bottom of each cylinder and this allows the continuous monitoring of the temperature inside the PBRs. PBRs are not equipped with any temperature control, but the greenhouse is air conditioned to avoid extreme temperatures. Temperature and pH values are registered and downloaded with the


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JUMO AQUIS touch S (equipped with the Evaluation Software PCA3000), which is a modular multichannel measuring device for liquid analysis with integrated controller. On the top of each PBR there is a high efficiency monocrystalline silicon cell (Litemeter PAR Current, SoluzioneSolare, Vicenza, VI, Italy) as sensor for the detection of the sunlight natural illumination rate collected in continuous mode. Data collection occurs via the connection with a data logger Stylitis-10 (Symmetron, Greece). In particular, every ten minutes of continuous measurements, a mean value is registered. This allows the collection of all the fluctuations of light intensity due to the day/night cycle, but also to instant weather conditions. The system was customised for this project in collaboration with SoluzioneSolare and calibrated with theLI-250A photometer already utilised for lab scale cultures. Since the PBRs are directly exposed to natural sunlight, the illumination rate and the temperature experienced by the algae growing in the PBRs are dependent on those relative to the seasons. However, the position of the sensors and the fact that they collect mostly beams orthogonal to their surface make so that after noon, when the sun


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is on the right side of the plant, the sensors measure a lower light intensity value with respect to the actual one absorbed by the culture.

Figure 1. Cultivation system used for this project, made by two vertical bubble columns with different volumes. From left to right: 5L – 0.07m diameter and 42L – 0.21m diameter; pH1 and pH2: pH probes; LS1 and LS2: light sensors; T1 and T2: temperature probes.

Software


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The simulations and parametric estimations are carried out using the process modelling environment gPROMSTM Model Builder 4.1 version by Process System Enterprise Ltd. (London, UK).

3. The modelling approach A mathematical model is developed to simulate and optimise the evolution of the biomass concentration inside the culture. Under the assumption of a perfectly mixed culture, the total biomass balance can be represented by the following equation: d[𝐶𝑏(t) ∙ 𝑉(t)] dt

= 𝐺(·)𝑉(t) ― 𝑅(·)𝑉(t) ― 𝐶𝑏(t)𝑞𝑜𝑢𝑡(t)

(2)

where G(·) is the biomass growth function and R(·) is the respiration function. The harvest of biomass is given by the product between the biomass concentration Cb(t) and the volumetric flowrate 𝑞𝑜𝑢𝑡(t) extracted by the reactor. V(t) is the culture volume and varies over time according to: d𝑉(t) dt

(3)

= 𝑞𝑖𝑛(t) ― 𝑞𝑜𝑢𝑡(t)

where 𝑞𝑖𝑛 is the inlet fresh medium flowrate. Equation 3 describes the variation of the culture volume due to the operations of harvesting and dilution; note that both


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harvesting and dilution are fast operations, even if manually processed, lasting only few minutes.

Growth model The growth term G(·) can be represented as the product of the biomass concentration

Cb and the specific growth rate μ [s-1], which is strongly influenced by the environmental conditions, mainly light and temperature. In the literature several modelling approaches were proposed to describe microalgae growth17,18. Our selection was mainly based on the possibility to represent the key phenomena considering the limited number of measured variables (light, temperature and biomass concentration). We adopted the formulation developed by Molina Grima et al.19, successively improved by AciénFernández et al.20 to account for photoinhibition: 𝑎+

𝐼𝑎𝑣

𝜇 = 𝜇𝑚

𝑏 𝑎+ 𝐼𝑤𝑚 𝐼𝑤𝑚 𝑚 𝐾𝐼

( ( )) 𝐼′𝑘 +

𝑏 𝐼𝑤𝑚

𝑎+

+ 𝐼𝑎𝑣

(4)

𝑏 𝐼𝑤𝑚

where Iwm [μmol/(m2s)] is the mean incident radiation on the reactor surface and Iav [μmol/(m2 s)] is the average radiation inside the reactor. The model has six parameters: the maximum specific growth rate μm [s-1]; parameters a and b[-] that are used to


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represent through a linear correlation depending on Iwm the exponential law assessing the impact of equipment geometry on light-related variables Iav and Iwm; the specific irradiance constant Ik’ [μmol/(m2 s)], the photoinhibition constant KI [μmol/(m2 s)]; and a photoinhibition modelling factor m [-]. In the original work20, the mean incident radiation Iwm was calculated by averaging a whole daylight period. Here, Iwm is instead calculated by averaging the measured incident radiation over a (shorter) period of 90 minutes. Furthermore, the original model is simplified neglecting the linear relationship on Iwm in the exponent; thus our model becomes as follows:

𝜇 = 𝜇𝑚

𝐼𝑛𝑎𝑣 𝑛 𝐼𝑤𝑚 𝑚 𝐾𝐼

( ( )) 𝐼′𝑘 +

(5) + 𝐼𝑛𝑎𝑣

where n [-] now represents the equipment geometry factor.

Average irradiance calculation Model (5) requires to define the average radiation inside the reactor Iav. Light intensity is not constant along the reactor radius principally due to a self-shading effect between cells and this determines an internal photosynthetic rate profile determined by the light


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distribution inside the culture. Bearing this in mind, it is possible to model the light intensity distribution inside the culture given a few parameters: the environmental irradiance intensity I0, the biomass concentration, the extinction coefficient Ka of the specific organism and the geometrical features of the reactor. The approach applied in this work is based on the Lambert-Beer law and was originally developed for parallelepiped-shape geometries but can be extended to different geometries via a discretisation of the actual volume21.

The average irradiance Iav along a parallelepiped can be calculated as: 𝐼0

(6)

𝐼𝑎𝑣 = 𝐿𝐾𝑎𝐶𝑏(1 ― e ―𝐿𝐾𝑎𝐶𝑏)

Integrating this equation over the whole cylinder volume, the average irradiance along the culture results to be: 2𝐼0

(

π

)

𝐼𝑎𝑣 = π𝑟𝐾𝑎𝐶𝑏 1 ― ∫02 cos (ϕ)e ―2𝑟𝐾𝑎𝐶𝑏cos (ϕ)dϕ

(7)

where r is the reactor radius. The value used for the extinction coefficient is 0.08 m2/g, as reported in literature for similar microalgae species22. Using this equation it is possible to estimate the irradiance without direct measurements inside the culture.


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Respiration contribution The respiration term R(·) can be represented as the product of the biomass concentration and the respiration rate λ[s-1] of the organism: (8)

𝑅(·) = 𝜆𝐶𝑏(t)

Temperature dependence Temperature has a severe impact on the capability of photosynthetic organisms of exploiting light and therefore its effect must be considered when modelling biological systems. The major influence is observed on growth, respiration and photoinhibition14. Following the work by Bernard and Remond23, temperature effects are here represented using a hyperbolic corrective function:

Φ(𝑇𝑟) =

{

(𝑇𝑟 ― 𝑇𝑚𝑎𝑥)(𝑇𝑟 ― 𝑇𝑚𝑖𝑛)2 (𝑇𝑜𝑝𝑡 ― 𝑇𝑚𝑖𝑛)[(𝑇𝑜𝑝𝑡 ― 𝑇𝑚𝑖𝑛)(𝑇𝑟 ― 𝑇𝑚𝑖𝑛) ― (𝑇𝑜𝑝𝑡 ― 𝑇𝑚𝑎𝑥)(𝑇𝑜𝑝𝑡 + 𝑇𝑚𝑖𝑛 ― 2𝑇𝑟],

0,

𝑖𝑓 𝑇𝑚𝑖𝑛 < 𝑇𝑟 ≤ 𝑇𝑚𝑎𝑥 (9) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

where Tr [°C] is the reactor temperature (assumed to be uniform through the geometry), while parameters Tmin, Topt, and Tmax represent the minimum, optimal, and maximum growth temperature, respectively.


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Considering also the correction on temperature, the growth and respiration rates are modified as follows:

𝐺(·) = 𝜇𝑚

𝐼𝑛𝑎𝑣

𝐶𝑏(t)Φ(𝑇𝑟)

𝑚 𝑛

( ( )) 𝐼′𝑘 +

𝐼𝑤𝑚

𝐾𝐼Φ(𝑇𝑟)

(10)

+ 𝐼𝑛𝑎𝑣

(11)

𝑅(·) = 𝜆𝐶𝑏(t)Φ(𝑇𝑟)

4. Model calibration The model (eqs 2,3,7, 9-11), has nine parameters to be estimated: θ= [𝐼′𝑘; 𝑚; 𝑛; 𝐾𝐼; 𝜇𝑚 ; 𝜆; 𝑇𝑚𝑖𝑛; 𝑇𝑜𝑝𝑡; 𝑇𝑚𝑎𝑥]. Since the same organism is cultivated in both reactors, the model can be calibrated (identified) considering only one reactor (42L PBR is chosen for the purpose). Only parameter n, i.e. the geometry factor, which depends on the PBR geometrical features, will be recalibrated when 5L PBR will need describing. This will also serve as a proof that the calibrated model parameters are indeed representative of the microalgae biological response and do not incorporate significant information deriving from the specific cultivation system. First of all, it is essential to verify whether the model parameters can be estimated based on available measurements. Sensitivity analysis is a simple and effective


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methodology that can be performed to the scope, at least to assess if practical identifiability issues may arise24. The sensitivity qik of the ith response to the kth model parameter is defined as: ∂𝑦𝑖

𝑞𝑖𝑘 = ∂𝜃𝑘 ≈

𝑦′𝑖 ― 𝑦𝑖 ∆𝜃𝑘

𝑖 = 1…NM, 𝑘 = 1…Nθ

(12)

where NM is the total number of measurements, Nθ is the total number of model parameters, yi is the ith measured responses predicted by the model, y′ is the same response obtained from a perturbed value of the kth parameter θk, and Δθk is the perturbation. Since the only measured response here is the biomass concentration, equation (12) becomes:

𝑞𝑘 =

𝐶′𝑏 ― 𝐶𝑏

(13)

∆𝜃𝑘

Perturbation Δθk is set equal to 1% of the parameter guess value. The guess values of the model parameters are those reported in literature for similar organisms and are listed in Table 1.Typical light and temperature profiles during a generic week are used as inputs to the model to run the sensitivity analysis. Results are shown in Figure 2.

Table 1. Guess values of the parameters used for the sensitivity analysis for 42L PBR.


17


Guess

Bibliographic

value

Reference

𝐼′𝑘 [μmol/(m2 s)]

225

22

𝐾𝐼[μmol/(m2 s)]

768.40

20

𝑚

3.04

20

𝑛

2.02

22

𝜇𝑚[s-1]

2.08·10-5

14

𝜆[s-1]

2.01·10-6

14

𝑇𝑚𝑖𝑛[°C]

0.75

25

𝑇𝑜𝑝𝑡[°C]

31.85

25

𝑇𝑚𝑎𝑥[°C]

34.85

25

Parameter

Page 18 of 46

Figure 2. Results of the sensitivity analysis performed on the growth parameters (a) and temperature parameters (b).


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Despite showing a good sensitivity on most parameters, it is possible to notice that the biomass concentration is not significantly affected by a variation of KI and m. In fact, the impossibility to identify KI can be explained by the fact that the reactors, and particularly the 42L one, are likely to operate in light-limited conditions: even with a full sunlight, available light intensity becomes limiting after the first layer (~1 cm) of culture and thus most of the cells are expected to be light limited27. As a result photoinhibition is estimated to affect only the first, more exposed cells and for a few hours a day. Also the minimum growth temperature Tmin has no impact on biomass concentration (this is likely due to the fact that the culture never experiences a temperature close to the actual Tmin value) so no information is contained in the experiments. We verified that indeed it was impossible to estimate the three parameters in a satisfactory way from available experimental data (see Appendix A). Their values were therefore set by retaining the literature values of Table 1. Note that the fact that no estimation on KI was possible may determine some uncertainty on the model capability to predict photoinhibition effects, although no clear indication in this respect will appear in the calibration and validation tests.


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Model calibration The parameter estimation is carried out within the modelling environment gPROMSTM using the Maximum Likelihood method. To mitigate the risk of incurring into local minima, a multiple shooting technique26 was applied so that the optimisation problem was solved with different guesses for the initial parameter values. The final values are reported in Table 2, coupled with the statistical analysis on the estimation. It can be observed that all parameters are estimated in a statistically satisfactory way. The fitting of experimental data after model calibration is reported in Figure 3.

Table 2. Results of the parameters estimation procedure performed for 42L PBR with the confidence interval and t-values. An estimate is considered satisfactory if the final tvalue is above the reference t-value. Parameter

Value

Confidence interval t-value (95%)


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(95%) 𝐼′𝑘 [μmol/(m2 s)]

217.40

±25.65

8.49

𝑛

2.125

±0.46

4.62

𝜇𝑚[s-1]

8.06·10-5

±1.14·10-5

7.11

𝜆[s-1]

7.49·10-6

±2.27·10-6

3.32

𝑇𝑜𝑝𝑡[°C]

34.27

±3.6

9.51

𝑇𝑚𝑎𝑥[°C]

36.756

±4.9

7.53

Reference t-value (95%):

1.83

Figure 3. Model trajectory obtained at the end of the model calibration on 42L PBR. Experimental data were collected between June 18th and 21st, 2018. The quality of the fitting is evaluated by a comparison of the weighted residuals and the critical χ2-value (which is supposed to be lower than the residuals for the estimation


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to be satisfactory). In this experiment the residuals are equal to 9.67 with a critical χ2value of 11.07.

Figure

4.

Model

validation

on

different

experiments

performed

at

different

concentrations. Experimental data were collected between between July 2nd and 9th (a) and between May 28th and 30th (b), 2018. Different experimental data were used to validate the model. Two examples are shown in Figure 4, where the calibrated model is used to simulate the biomass evolution during two different experiments performed between July 2nd and 9th (a) and between May 28th and 30th(b).

5L PBR The same model was also used to simulate the second cultivation reactor, i.e. 5L PBR. Only the geometry factor n was identified using experimental data from 5L PBR.


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The new value for the geometry factor is 1.31±0.086 with a t-value of 15.21 (versus a reference t-value of 2.02). Figure 5 shows the good agreement between the experimental data and the model predictions (the weighted residuals are 10.58 versus a critical χ2-value of 11.07), thus demonstrating the generality of the calibrated growth model, which can be scaled-up or -down simply by adjusting a geometry parameter.

Figure 5. Model trajectory obtained for 5L PBR. Experimental data were collected during the week between June 18th and 21st, 2018

5. Operation optimisation The calibrated model was then used to propose an optimised operation strategy to increase productivity. Productivity is here defined as the sum of the harvested biomass


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plus biomass remaining inside the reactor at the end of a pre-set time horizon. The objective function is defined as follows: max 𝑃𝑛𝑒𝑡 = max [𝑉𝑓𝐶𝑏, 𝑓 + 𝑡∑𝑞𝑗𝑜𝑢𝑡𝐶𝑏,𝑗] 𝑜𝑢𝑡

𝑞

𝑗 = 1…N𝑑𝑖𝑙

(14)

𝑜𝑢𝑡

𝑞

where Ndil is the total number of dilutions performed during the time horizon, while Vf and Cb,f refer to PBR volume and biomass concentration at the end of the time horizon. The only variable that can be optimised is flowrate 𝑞𝑜𝑢𝑡, which is assumed to vary within range [0; 𝑞𝑚𝑎𝑥], where 𝑞𝑚𝑎𝑥 is the value running the reactor empty in time t. The inlet flowrate (dilution) is always set equal to the outlet one so that the PBR volume does not change. The harvesting time t is constant and assumed to be equal to 1 s. This is not realistic (harvesting and dilution take about 10 minutes, without considering the time needed to measure the biomass before and after the dilutions and to prepare the material for the dilution), but considering the time scale of the process this has very little effect and the advantage is that the calculated flowrate [m3/s] is numerically identical to the harvest volume [m3]. The harvest operations can be scheduled every 2


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hours (this is the time assumed to be compatible with the experimental practice) from 10 am until 6 pm (5 times per day). Four optimisation problems were solved, one for each season of the year (spring, summer, autumn, winter). Each season is simulated implementing the mean daily values of temperature and incident radiation as measured in our facility during a reference period (April for spring, August for summer, October for autumn, and January for winter). The optimisation time horizon is set as 8 days but the results only refer to the central 5 days so as to neglect the transitional period related to the chosen initial conditions, and the fact that at the end of the optimisation period the solver always proposes to empty the PBR to maximise biomass harvest. The optimisation is carried out for both PBRs. Software gPROMSTM is used to solve the dynamic optimisation problem.

42L PBR Figure 6 reports the solution obtained at the end of the optimisation task in terms of biomass trajectory that should be followed. As expected, summer is characterised by the best condition for growth in terms of environmental conditions and for this reason it


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shows the highest allowed biomass concentration before the dilution (around 200 g/m3). Spring and autumn have instead worse conditions, clearly represented by the fact that, in order to have an appreciable growth, the culture should be diluted down to a lower concentration (90 g/m3 and 48 g/m3, respectively) to allow a good light penetration all along the reactor width. Although a minimal growth is experimentally found in winter, too, the optimisation policy is simply that of no-harvest during the time horizon (and therefore results are not reported).


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Figure 6. Biomass concentration trajectory inside 42L PBR (a, b, c)and volume to be harvested (d, e, f) obtained as solution of the optimisation problem. The plots refer to spring (a, d), summer (b, e) and autumn (c, f).

A general consideration that can be made after a visual inspection of the plots in Figure 6 is that the dilution should be performed when respiration becomes predominant with respect to growth in order to minimise the biomass loss during this process. For this specific reactor, respiration becomes predominant around noon, counterintuitively with what one would expect. This is due to the position of the reactor inside the greenhouse: after midday, the reactor does not receive enough light to allow a rapid growth of the cells. This confirms the hypothesis of light-limited growth conditions. Although the PBR position is certainly suboptimal, it is a good result that the optimisation solution takes into account the actual experimental setting. Volumes to be harvested are those allowing the culture to reach again the pre-dilution concentration within 24 hours and to reach a sort of steady-state during the operating life of the plant. They are strongly linked to the environmental conditions and to the capability of the culture to generate new biomass. Indeed, in summer half of the biomass can be


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extracted because the available light makes so that within one day the culture is able to double up the concentration getting to the pre-dilution condition. In spring and autumn this capability is decreased due to the decreased light intensity and so, in order to avoid the culture wash-out, less volume (i.e. biomass) can be extracted. It is interesting to observe that only one harvest per day is assumed to be the optimal operation, which is exactly what is carried out in the current cultivation practise as a result of a trial and error “optimisation”, based on the operator’s experience. The key difference with respect to current practice is the dilution time (anticipated by 5 hours) and the volume that is harvested (in fact, in Summer the optimised harvesting volume is the same as the one currently collected, whereas in Spring and Autumn it is halved due to the reduced productivity). Even if comparisons are always complex because of many differences in geometries, growing conditions, strains, etc. it is worth underlying that productivity obtained from 42L PBR presented in this work (200g/m3) is consistent with that found by Doria et al29 for Scenedesmus acutus grown in an outdoor vertical bubble column. This was significant also because in our case the amount of photons/day


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reaching the reactor surface was lower than in Doria et al29, supporting again the idea that the PBR was under limiting light for an optimal algae growth.

5L PBR The results obtained for the smaller 5L PBR reported in Figure 7 have the same rationale of those referred to 42L PBR, i.e. the dilution before the respiration period, which in this case is predominant after 2pm. Also in this case the highest concentrations are obtained in Summer (around 510 g/m3 before the dilution), but, in this case, the simulator suggests that the dilution should not be operated in one single harvest but with one main extraction followed by one or two minor dilutions.


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Figure 7. Optimised biomass concentration trajectory and volume to be harvested for 5L PBR in spring (a, d), summer (b, e) and autumn (c, f). As for 42L reactor, also in this case growth does not take place in winter.

The biomass concentration in 5L PBR is higher than in 42L PBR due to the smaller reactor diameter, which determines a decrease in the light path and allows a better light penetration also with highly concentrated cultures. Table 3 shows a comparison of the predicted productivity with the two dilution policies: it is clearly visible that the optimised procedure allows a sensible increase in the productivity of both reactors during each season. For the 42L PBR the highest increase with respect to current practise is


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achieved in Summer (+46.8%), while for 5L PBR the highest increase occurs in autumn (+73%), when a clearer suspension allows a very good light exploitation also in the inner part of the culture. Table 3. Comparison between the productivity theoretically achievable with the optimised dilution policy and that achieved adopting the old policy (simulated results). The measured productivity refers to a time horizon of 5 days. 42 L PBR Season

Optimised productivity [g]

5L PBR Old productivity

% increase

[g]

Optimised

Old

productivity

productivity

[g]

[g]

% increase

Spring

12.18

9.91

22.9

5.06

4.57

10.7

Summer

24.53

16.71

46.8

7.25

5.59

29.7

Autumn

4.12

3.08

33.8

3.96

2.29

73.0

Experimental validation The developed procedure was tested experimentally to assess if the simulated results are consistent with the experimental response. Two different experiments were performed in two different periods: the first one in the week between July 30th and August 3rd, the second one between October 1st and 5th. The comparison is thus made


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with the productivity obtained during a week characterised by similar values of culture temperature, incident radiation and concentration and during which the dilutions were performed following the non-optimised procedure. We could find a reasonable analogue only for the summer period, since October 2018 was unusually hot and sunny. Table 4 contains a summary of the obtained results for the period in the study.

Table 4.Experimental values of productivity obtained with the new dilution policy compared with that achieved during a similar period with the old policy. 42L PBR Season

Optimised productivity [g]

5L PBR Old productivity

% increase

[g]

Optimised

Old

productivity

productivity

[g]

[g]

% increase

Summer

17.0

14.4

17.78

11.4

9.3

21.76

Autumn

12.4

-

-

9.8

-

-

Regarding the test performed in summer, both reactors showed a significant increase in productivity, although not as good as suggested by the theoretical optimisation.


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However, it is important to keep in mind that the results only represent an approximated experimental assessment of the optimisation procedure. In fact, since no parallel equipment is available, the optimised policy and the current one could not be implemented simultaneously. The comparison was carried out by looking for a “similar” week within the historical database of experimental conditions, but quite obviously no perfectly identical weeks in terms of light and temperature dynamics could be found. For instance, as already anticipated, productivity in the Autumn test was much higher than expected, due to particularly favourable weather conditions, and no similar historical data were available. Besides, the optimisation problem was solved considering average seasonal conditions; however, small variations (e.g. weather) occurring on some days may affect the experimental response, significantly28. As a consequence, we expect that real-time optimisation would have produced a different (more effective) harvesting policy. Having said, results are positive and demonstrate that the efficacy of a modelbased approach to improve process operation and to increase biomass productivity without any additional cost in terms of equipment and/or instrumentation. Furthermore, the possibility to predict the production system performance in a reliable way may pave


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the way to more sophisticated technological solutions and operation policies, e.g. by using (optimised) artificial illumination substituting (or supporting) solar radiation, particularly during the seasons at low light intensities.

Temperature optimisation Temperature control can be used to enhance productivity30. Although this is not possible in the available experimental facilities, the optimisation problem was solved to evaluate the theoretical optimal temperature profile to be kept inside the culture and to assess the potential productivity improvement. The light intensity profile used in the simulation is the one measured during a generic day in summer (as considered in the previous optimisation problem) and the problem is solved referring to 42L PBR. The range of temperature is set between [15; 40] °C, which represents extreme values effectively measured in the facility. The resulting optimal temperature profile is shown in Figure 8.


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Figure 8. Optimal daily temperature profile (solid line) to be followed in order to enhance biomass productivity in 42L PBR; the dashed line represents the optimal growth temperature.

As one would reasonably expect, during the period of the day when growth prevails on respiration, the temperature has to be kept as close as possible to the optimal growth value. When, instead, the light intensity is low so as to make respiration prevail on growth, the culture temperature must be decreased to slow down the metabolic cycle and diminish the biomass loss (this is consistent to what found by De-Luca et al.14). This optimal temperature profile leads to doubling the maximum biomass concentration achievable in the reactor, as suggested by a comparison between the simulated biomass evolutions with and without temperature control (Figure 9).


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Figure 9. Comparison between the biomass trajectory with the mean seasonal values of temperature (blue line) and that achievable with a temperature control (red line).

Solving the dilution optimisation problem with the optimal temperature profile resulted in the same dilution schedule obtained in the previous case, except for the values of the concentrations to be achieved after dilution, which are in this case around 170 g/m3 (with respect to 125 g/m3 for the culture without temperature control) as reported in Figure 10. The productivity theoretically achievable is 34.04 g of biomass, with a further increase of 38.8% with respect to the optimised policy without temperature control, and of 103.7% with respect to the current dilution procedure. Clearly, temperature control would require some significant modification in equipment design (e.g. inserting a


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refrigeration coil or recirculating the solution through an external heat exchanger), which would likely have additional effects on the productivity performance.

Figure 10. Comparison between the optimised dilution policy obtained with (red line) and without (blue line) a temperature control for the culture.

6. Conclusions A mathematical model representing the growth dependence of Scenedesmus sp. cultures on light and temperature was rigorously calibrated on experimental data from outdoor cylindrical pilot photobioreactors. The calibrated model was used to define an optimised harvesting policy in the batch operation of the pilot plant. Both simulated and experimental results demonstrated the effectiveness of the proposed approach and the


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advantage of model-based optimisation with respect to heuristics based on trial-anderror experimental tests. Simulations also suggested that the implementation of an optimal temperature control strategy could improve productivity dramatically. Future work will aim at extending experimental validation and to propose a framework for real-time model-based optimisation based on actual weather conditions.

Appendix A The sensitivity analysis states that two model parameters cannot be estimated with a sufficient precision exploiting only the available experiments. In Table A.1 the results of the estimation exercise are reported, confirming that no parameter could be estimated in a reliable way.

Table A.1. Estimation attempt performed for the parameters related to photoinhibition.

Parameter

Value

Confidence interval (95%)

t-value (95%)

𝐾𝐼[μmol/(m2 s)]

2499.91

±1.29·106

0.0019

𝑚

0.25

±69.65

0.0036

𝑇𝑚𝑖𝑛

13.49

±18.33

0.7362

Reference t-value (95%):

1.74


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AUTHOR INFORMATION

Corresponding Author *Fax: +39.049.827.5461. E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

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Graphical abstract


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Model-Based Optimization of Microalgae Growth in a Batch Plant

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