# 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

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## 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.

## 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

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