# A Two-Stage System for the Large-Scale Cultivation of Biomass: a Design and Operation Analysis Based on a Simple Steady-State Model Tuned on Laboratory Measurements

## Abstract

The optimal design and operation at large scale of a continuous fermentation process including a biological reactor/photobioreactor and a gravity settler with partial recycle and purge of the biomass are addressed. The proposed method is developed with reference to microalgae (*Scenedesmus obliquus*) cultivation, but it can be applied to any fermentation process as well as to activated sludge wastewater treatment. A procedure is developed to predict the effect of process variables, mainly the recycle ratio (*R*), the solid retention time (*θ*_{ c }), the reactor residence time (*θ*), and the ratio between feed and purge flow rates (*F*_{ I }/*F*_{ W }). It includes a simple steady-state model of the two units coupled in the process and the experimental measurement of basic kinetic data, in both the bioreactor and the settler, for the tuning of model parameters. The bioreactor is assumed as perfectly mixed, and a rigorous gravity-flux approach is used for the settler. The process model is solved in terms of dimensionless variables, and plots are given to allow sensitivity analyses and optimization of operating conditions. A discussion about washout is presented, and a simple method is outlined for the calculation of the minimum values of residence time (*θ*_{ min }) and recycle ratio (*R*_{ min }) and of the maximum allowed recycle ratio (*R*_{ max,operating }) and biomass purge rate (*F*_{ Wmax })*.* In particular, it is shown that the system is sensitive to the concentration of biomass lost from the top of the settler (*C*_{ X }^{ S }). The proposed method can be useful for the design and analysis of large-scale processes of this type.

## Keywords

Fermentation Microalgae Operating variables Gravity settler New analysis method## Abbreviations

*I, E, U, S, R*and*W*When associated with variables cited below they refer to the streams of the process including a reactor and settler, as represented in Fig. 1.

*C*_{i}Concentration of component

*i*(g L^{−1}or kg m^{−3}for solid concentration)*θ*Residence time or hydraulic retention time (HRT) (day)

*r*_{i}Rate of production or consumption of component

*i*(g L^{−1}day^{−1})*K*_{M}Monod saturation constant for substrate (g L

^{−1})*k*Maximum specific growth rate (day

^{−1})*k*_{d}Specific rate of cell death (day

^{−1})*F*It indicates the volumetric flow rates of the different streams in the process

*M*It indicates the mass flow rates of the different streams in the process (kg day

^{−1})*F*_{W}Cell purge flow rate (m

^{3}day^{−1})*F*_{R}Recycle flow rate (m

^{3}day^{−1})*F*_{I}Inlet flow rate (m

^{3}day^{−1})*θ*_{c}Solid retention time (SRT) (day)

- \( {\theta}_c^{wo} \)
Wash-out time for SRT (day)

*Y*_{X/S}Apparent yield coefficient for substrate-to-biomass conversion (g g

^{−1})*V*_{R}Effective volume of the reactor (m

^{3})*R*_{min}Minimum recycle ratio (−)

*R*_{max,operating}Maximum recycle ratio that permits an adequate settler operation (efficient sedimentation), considering

*v*= 0 at the bottom of the settler*R*_{C}Critical recycle ratio, i.e., maximum recycle ratio to permit that the settler does not collapse

*G*_{u}Convective solid flux in the settler (kg m

^{−2}day^{−1})*G*_{v}Gravitational solid flux in the settler (kg m

^{−2}day^{−1})- G
_{app} Applied solid flux in the settler (kg m

^{−2}day^{−1})*u*Convective settling velocity

*A*Settler surface area

*v*Gravity settling velocity (m h

^{−1})

## Notes

### Acknowledgements

The authors thank CNPq, Brazil (National Research Council of Brazil)—Process number 249182/2013-0—for resources and fellowship.

### Funding

This study was funded by CNPq, Brazil (National Research Council of Brazil) Process number 249182/2013-0.

### Compliance with Ethical Standards

### Conflict of Interest

The authors declare that they have no conflict of interest.

### Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

## Supplementary material

## References

- 1.Petre E, Selisteanu D (2013) A multivariable robust-adaptative control strategy for a recycled wastewater treatment bioprocess. Chem Eng Sci 90:40–50CrossRefGoogle Scholar
- 2.D’Antonio G, Carbone P (1987) Verifica sperimentale della teoria del flusso solido. Ing Sanit 325–336Google Scholar
- 3.Sardo F, Indelicato S (1995) Verifica della teoria del flusso solido in un impianto a fanghi attivi a portata costante. Ing Ambient 24(10):584–587Google Scholar
- 4.Yuan Q, Sparling R, Oleszkiewicz JA (2009) Waste activated sludge fermentation: Effect of solids retention time and biomass concentration. Water Res 43:5180–5186CrossRefPubMedGoogle Scholar
- 5.Alcantara C, Dominguez JM, Garcia D, Blanco S, Perez R, Garcia-Encina PA, Munoz R (2015) Evaluation of wastewater treatment in a novel anoxic-aerobic algal-bacterial photobioreactor with biomass recycling through carbon and nitrogen mass balances. Bioresour Technol 191:173–186CrossRefPubMedGoogle Scholar
- 6.Amanatidou E, Samiotis G, Bellos D, Pekridis G, Trikoilidou E (2015) Net biomass production under complete solids retention in high organic load activated sludge process. Bioresour Technol 182:193–199CrossRefPubMedGoogle Scholar
- 7.Nges IA, Liu J (2010) Effects of solid retention time on anaerobic digestion of dewatered-sewage sludge in mesophilic and thermophilic conditions. Renew Energy 35:2200–2206CrossRefGoogle Scholar
- 8.Lee I, Parameswaran P, Rittmann BE (2011) Effects of solid retention time on methanogenesis in anaerobic digestion of thickened mixed sludge. Bioresour Technol 102:10266–10272CrossRefPubMedGoogle Scholar
- 9.Narodolawsky M, Mittmannsgruber H, Nagl W, Moser A (1988) Modelling of alcohol fermentation in a tubular reactor with high biomass recycle. Bioprocess Eng 3:135–140CrossRefGoogle Scholar
- 10.Oliveira SC, Castro HF, Visconti AES, Giudici R (2015) Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle. Bioprocess Biosyst Eng 38:469–479CrossRefPubMedGoogle Scholar
- 11.Meyer CL, Papoutsakis ET (1989) Continuous and biomass recycle fermentations of
*Clostridium acetobutylicum*. Bioprocess Eng 4:49–55CrossRefGoogle Scholar - 12.Lee D, Li V, Noike T (2010) Influence of solids retention time on continuous H
_{2}production using membrane bioreactor. Int J Hydrog Energy 32:52–60CrossRefGoogle Scholar - 13.Grøn S, Morcel C, Emborg C, Biedermann K (1995) Cell recycling studies for α-amylase production by Bacillus amyloliquefaciens. Bioprocess Eng 14:23–31CrossRefGoogle Scholar
- 14.Grøn S, Biedermann K, Emborg C (1996) Production of proteinase A by Saccharomyces cerevisiae in a cell-recycling fermentation system: experiments and computer simulations. Appl Microbiol Biotechnol 44:724–730CrossRefPubMedGoogle Scholar
- 15.Park JBK, Craggs RJ, Shilton AN (2011) Recycling algae to improve species control and harvest efficiency from a high rate algal pond. Water Res 45:6637–6649CrossRefPubMedGoogle Scholar
- 16.Sforza E, Gris B, Silva CEF, Morosinotto T, Bertucco A (2014) Effects of light on cultivation of
*Scenedesmus obliquus*in batch and continuous flat plate photobioreactor. Chem Eng Trans 38:211–216Google Scholar - 17.Sing SF, Isdepsky A, Borowitzka MA, Lewis DW (2014) Pilot-scale continuous recycling of growth medium for the mass culture of a halotolerant
*Tetraselmis sp.*in raceway ponds under increasing salinity: a novel protocol for commercial microalgal biomass production. Bioresour Technol 161:47–54CrossRefGoogle Scholar - 18.Depraetere O, Pierre G, Deschoenmaeker F, Bodri H, Foubert I, Leys N, Markou G, Wattiez R, Michaud P, Muylaert K (2015) Harvesting carbohydrate-rich
*Arthrospira platensis*by spontaneous settling. Bioresour Technol 180:16–21CrossRefPubMedGoogle Scholar - 19.Kosinska K, Miskiewicz T (2009) Performance of an anaerobic bioreactor with biomass recycling continuously removing COD and sulphate from industrial wastes. Bioresour Technol 100:86–90CrossRefPubMedGoogle Scholar
- 20.Uduman N, Qi Y, Danquah MK, Forde GM, Hoadley A (2010) Dewatering of microalgal cultures: a major bottleneck to algal-based fuels. J Renewable Sustainable Energy 2:12701–12715CrossRefGoogle Scholar
- 21.Park JBK, Craggs RJ, Shilton AN (2013) Enhancing biomass energy yield from pilot-scale high rate algal ponds with recycling. Water Res 47:4422–4432CrossRefPubMedGoogle Scholar
- 22.Zhu L (2015) Biorefinery as a promising approach to promote microalgae industry: an innovative framework. Renew Sust Energ Rev 41:1376–1384CrossRefGoogle Scholar
- 23.Barros AI, Gonçalves AL, Simoes M, Pires JCM (2015) Harvesting techniques applied to microalgae: a review. Renew Sust Energ Rev 41:1489–1500CrossRefGoogle Scholar
- 24.Lund JWG (1951) A sedimentation technique for counting algae and other organisms. Hydrobiologia 3(4):390–394CrossRefGoogle Scholar
- 25.Salim S, Bosma R, Vermué MH, Wijffels RH (2011) Harvesting of microalgae by bio-flocculation. J Appl Phycol 23:849–855CrossRefPubMedGoogle Scholar
- 26.Smith BT, Davis RH (2012) Sedimentation of algae flocculated using naturally-available magnesium-based flocculants. Algal Res 1(1):32–39CrossRefGoogle Scholar
- 27.Liu J, Tao Y, Wu J, Zhu Y, Gao B, Tang Y, Li A, Zhang C, Zhang Y (2014) Effective flocculation of target microalgae with self-flocculating microalgae induced by pH decrease. Bioresour Technol 167:367–375CrossRefPubMedGoogle Scholar
- 28.Rawat I, Kumar RR, Mutanda T, Bux F (2013) Biodiesel from microalgae: A critical evaluation from laboratory to large scale production. Appl Energy 103:444–467CrossRefGoogle Scholar
- 29.Du J, McGraw A, Lorenz N, Beitle RR, Clausen EC, Hestekin JA (2012) Continuous fermentation of Clostridium tyrobutyricum with partial cell recycle as a long-term strategy for butyric acid production. Energies 5:2835–2848CrossRefGoogle Scholar
- 30.Bertucco A, Beraldi M (2014) Sforza E (2014) continuous microalgal cultivation in a laboratory-scale photobioreactor under seasonal day-night irradiation: Experiments and simulation. Bioprocess Biosyst Eng 37:1535–1542CrossRefPubMedGoogle Scholar
- 31.Silva CEF, Gris B, Bertucco A (2016) Simulation of microalgal growth in a continuous photobioreactor with sedimentation and partial biomass recycling. Braz J Chem Eng 33(4):773–781CrossRefGoogle Scholar
- 32.Fernandes BD, Mota A, Teixeira JA, Vicente AA (2015) Continuous cultivation of photosynthetic microorganisms: approaches, applications and future trends. Biotechnol Adv 33(6):1228–1245CrossRefPubMedGoogle Scholar
- 33.Barbera E, Sforza E, Bertucco A (2015) Maximizing the production of
*Scenedesmus obliquus*in photobioreactors under different irradiation regimes: experiments and modeling. Bioprocess Biosyst Eng 38:2177–2188CrossRefPubMedGoogle Scholar - 34.Rippka R, Deurelles J, Waterbury JB, Herdman M, Stainer RY (1979) Generic assignments, strain histories and properties of pure cultures of cyanobacteria. J Gen Microbiol 111: 1–61.Google Scholar
- 35.Sundstrom DW, Klei HE (1979) Wastewater treatment. The University of Connecticut - Prentice Hall, Englewood CliffsGoogle Scholar
- 36.Sforza E, Enzo M, Bertucco A (2013) Design of microalgal biomass production in a continuous photobioreactor: An integrated experimental and modeling approach. Chem Eng Res Des 92(6):1153–1162CrossRefGoogle Scholar
- 37.Borzani W (2001) In: Borzani W, Schmidell W, Lima UA, Aquarone E (Coords.) Biotecnologia Industrial: VOLUME 2—Biotecnologia Industrial., Bluche, Sao Paulo, 560 pGoogle Scholar
- 38.Bertucco A, Volpe P, Klei HE, Anderson TF, Sundstrom DW (1990) The stability of activated sludge reactors with substrate inhibition kinetics and solids recycle. Water Res 24(2):169–174CrossRefGoogle Scholar
- 39.Peperzak L, Colijn F, Koeman R, Grieskes WWC, Joordens JCA (2003) Phytoplankton sinking rates in the Rhine region of freshwater influence. J Plankton Res 25(4):365–383CrossRefGoogle Scholar
- 40.Caciki A, Bayramoglu M (1995) An approach to controlling sludge age in the activated sludge process. Water Res 29(4):1093–1097CrossRefGoogle Scholar
- 41.Bai S, Srikantaswamy S, Shivakumar D (2010) Urban wastewater characteristic and its management in urban areas—a case study of Mysore City, Karnataka, India. J Water Resour Prot 2:717–726CrossRefGoogle Scholar
- 42.Mittal A (2011) Biological wastewater treatment. Water Today, August: 32–44Google Scholar
- 43.MPCA (2002) Design flow and loading determination guidelines for wastewater treatment plants: water/wastewater technical review and guidance. Minnesota Pollution Control AgencyGoogle Scholar
- 44.Da Silva TL, Reis A (2015) Scale-up problems for the large scale production of algae. In: Das D (ed) Algal Biorefinery: an integrated approach. Springer, Cham, pp 125–149CrossRefGoogle Scholar
- 45.Gupta PL, Lee S, Choi H (2015) A mini review: photobioreactor for large scale algal cultivation. World J Microbiol Biotechnol 31(9):1409–1417CrossRefPubMedGoogle Scholar
- 46.Rawat I, Kumar RR, Mutanda T, Bux F (2013) Biodiesel from microalgae: a critical evaluation from laboratory to large scale production. J Appl Energy 103:444–467Google Scholar
- 47.Zhang T, Hu H, Wu Y, Zhuang L, Xu X, Wang X, Dao G (2016) Promising solutions to solve the bottlenecks in the large-scale cultivation of microalgae for biomass/bioenergy production. Renew Sust Energ Rev 60:1602–1614CrossRefGoogle Scholar
- 48.Woo SH, Jeon CO, Yun Y, Choi H, Lee C, Lee DS (2009) On-line estimation of key processes variables based on kernel partial least squares in an industrial cokes wastewater treatment plant. J Hazard Mater 161(1):538–544CrossRefPubMedGoogle Scholar
- 49.Bezzaoucha S, Marx B, Maquin D, Ragot J (2013) Non linear joint state and parameter estimation: application to a wastewater treatment plant. Control Eng Prat 21(10):1377–1385CrossRefGoogle Scholar
- 50.Busch J, Elixmann D, Kuhl P, Gerkens C, Schloder JP, Back HG, Marquadt W (2013) State estimation of large-scale wastewater treatment plants. Water Res 47(13):4774–4787CrossRefPubMedGoogle Scholar
- 51.Tomita RK, Park SW (2009) Evolutionary multi-objective optimization of an activated sludge process. Comput Aid Chem Eng 27:747–752CrossRefGoogle Scholar
- 52.Qiao J, Hou Y, Han H (2018) Optimal control for wastewater treatment process based on an adaptive multi-objective differential evolution algorithm. Neural Comput Applic 1–14. https://doi.org/10.1007/s00521-017-3212-4
- 53.Lou I, Zhao Y (2012) Sludge bulking prediction using principal component regression and artificial neural network. Math Probl Eng 2012:237693 17 pagesCrossRefGoogle Scholar
- 54.Simion C, Chenaru O, Florea G, Lozano JI, Nabulsi S, Reis M, Cassidy J (2016) Decision support system based on fuzzy control for a wastewater treatment plant. Int J Environ Sci 1:344–349Google Scholar
- 55.Samsudin SI, Rahmat MF, Wahab NA (2014) Nonlinear PI control with adaptive interaction algorithm for multivariable wastewater treatment process. Math Probl Eng 2014:475053 13 pagesCrossRefGoogle Scholar
- 56.Wahab HF, Katebi R, Villanova R (2012) Comparisons of nonlinear estimators for wastewater treatment plants. In: 20th Mediterranean Conference on Control & Automation (MED), Barcelona, Spain, July 3-6.Google Scholar