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Tools for improving feeding strategies in a SBR with several species

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Abstract

This paper analyzes feeding strategies in a sequential batch reactor (SBR) with the objective of reaching a given (low) substrate level as quickly as possible for a given volume of water. Inside the SBR, several species compete for a single substrate, which leads to a minimal time control problem in which the control variable is the feeding rate. Following Gajardo et al. (2008) SIAM J Control Optim 47(6):2827–2856, we allow the control variable to be a bounded measurable function of time combined with possible impulses associated with instantaneous dilutions. For this problem, the extremal trajectories of the singular arc type are characterized as the strategies used to maintain the substrate at a constant level. Since this optimization problem is difficult to solve, this characterization provides a valuable tool for investigating the optimality of various feeding strategies. Our aim is thus to illustrate the use of this tool by proposing potential optimal feeding strategies, which may then be compared with other more intuitive strategies. This aim was accomplished via several numerical experiments in which two specific strategies are compared.

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Acknowledgments

The authors thank Francis Mairet for his fruitful discussions on the topic of this paper. We also thank two anonymous reviewers who have substantially contributed to the improved quality of this revision. Supported by FONDECYT under Grant No. 1120239 (P. Gajardo), 1110888 (H. Ramírez) and 1130538 (J.C. Rodríguez), the BASAL Project (Centro de Modelamiento Matemático, Universidad de Chile), CONICYT Anillo ACT1106, project BIONATURE of CIRIC, INRIA–Chile, and UFAM-INCTMat Avanço Global e Integrado da Matemática Brasilera e Contribuções a Região, CAPES–Brasil.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Avda. España, 1680, Valparaiso, Chile

    Pedro Gajardo

  2. Departamento de Ingeniería Matemática, Universidad de Chile & Centro de Modelamiento Matemático, Universidad de Chile–CNRS, Casilla 170/3, Santiago, Chile

    Héctor Ramírez Cabrera

  3. Departamento de Matemáticas, Universidad de Valparaíso, Casilla, 5030, Valparaiso, Chile

    Julio C. Rodríguez

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  1. Pedro Gajardo
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  2. Héctor Ramírez Cabrera
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  3. Julio C. Rodríguez
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Correspondence to Héctor Ramírez Cabrera.

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Gajardo, P., Ramírez Cabrera, H. & Rodríguez, J.C. Tools for improving feeding strategies in a SBR with several species. Bioprocess Biosyst Eng 37, 63–70 (2014). https://doi.org/10.1007/s00449-013-1077-1

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  • DOI: https://doi.org/10.1007/s00449-013-1077-1

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