Modeling and optimization of algae growth

Anthony Richard Thornton, Thomas Weinhart, Onno Bokhove, Bowen Zhang, Dick M. van der Sar, Kundan Kumar, Maxim Pisarenco, Maria Rudnaya, Valeriu Savceno, Jens Rademacher, Julia Zijlstra, Alicja Szabelska, Joanna Zyprych, Martin van der Schans, Vincent Timperio, Frits Veerman

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

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Abstract

The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runo water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity. The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants. With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn.
Original languageUndefined
Title of host publicationProceedings of the 72nd European Study Group Mathematics with Industry
EditorsJ. Frank, R. van der Mei, A. den Boer, J. Bosman, N. Bouman, S. van Dam, C. Verhoef
Place of PublicationAmsterdam
PublisherC.W.I.
Pages54-85
Number of pages32
ISBN (Print)not assigned
Publication statusPublished - 2010

Publication series

Name
PublisherCWI

Keywords

  • METIS-274054
  • Algae growth
  • IR-75743
  • EWI-19034
  • Coupled odes
  • Optimization
  • Numerical solution
  • Steady state analysis

Cite this

Thornton, A. R., Weinhart, T., Bokhove, O., Zhang, B., van der Sar, D. M., Kumar, K., ... Veerman, F. (2010). Modeling and optimization of algae growth. In J. Frank, R. van der Mei, A. den Boer, J. Bosman, N. Bouman, S. van Dam, & C. Verhoef (Eds.), Proceedings of the 72nd European Study Group Mathematics with Industry (pp. 54-85). Amsterdam: C.W.I..
Thornton, Anthony Richard ; Weinhart, Thomas ; Bokhove, Onno ; Zhang, Bowen ; van der Sar, Dick M. ; Kumar, Kundan ; Pisarenco, Maxim ; Rudnaya, Maria ; Savceno, Valeriu ; Rademacher, Jens ; Zijlstra, Julia ; Szabelska, Alicja ; Zyprych, Joanna ; van der Schans, Martin ; Timperio, Vincent ; Veerman, Frits. / Modeling and optimization of algae growth. Proceedings of the 72nd European Study Group Mathematics with Industry. editor / J. Frank ; R. van der Mei ; A. den Boer ; J. Bosman ; N. Bouman ; S. van Dam ; C. Verhoef. Amsterdam : C.W.I., 2010. pp. 54-85
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title = "Modeling and optimization of algae growth",
abstract = "The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runo water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity. The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants. With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn.",
keywords = "METIS-274054, Algae growth, IR-75743, EWI-19034, Coupled odes, Optimization, Numerical solution, Steady state analysis",
author = "Thornton, {Anthony Richard} and Thomas Weinhart and Onno Bokhove and Bowen Zhang and {van der Sar}, {Dick M.} and Kundan Kumar and Maxim Pisarenco and Maria Rudnaya and Valeriu Savceno and Jens Rademacher and Julia Zijlstra and Alicja Szabelska and Joanna Zyprych and {van der Schans}, Martin and Vincent Timperio and Frits Veerman",
year = "2010",
language = "Undefined",
isbn = "not assigned",
publisher = "C.W.I.",
pages = "54--85",
editor = "J. Frank and {van der Mei}, R. and {den Boer}, A. and J. Bosman and N. Bouman and {van Dam}, S. and C. Verhoef",
booktitle = "Proceedings of the 72nd European Study Group Mathematics with Industry",

}

Thornton, AR, Weinhart, T, Bokhove, O, Zhang, B, van der Sar, DM, Kumar, K, Pisarenco, M, Rudnaya, M, Savceno, V, Rademacher, J, Zijlstra, J, Szabelska, A, Zyprych, J, van der Schans, M, Timperio, V & Veerman, F 2010, Modeling and optimization of algae growth. in J Frank, R van der Mei, A den Boer, J Bosman, N Bouman, S van Dam & C Verhoef (eds), Proceedings of the 72nd European Study Group Mathematics with Industry. C.W.I., Amsterdam, pp. 54-85.

Modeling and optimization of algae growth. / Thornton, Anthony Richard; Weinhart, Thomas; Bokhove, Onno; Zhang, Bowen; van der Sar, Dick M.; Kumar, Kundan; Pisarenco, Maxim; Rudnaya, Maria; Savceno, Valeriu; Rademacher, Jens; Zijlstra, Julia; Szabelska, Alicja; Zyprych, Joanna; van der Schans, Martin; Timperio, Vincent; Veerman, Frits.

Proceedings of the 72nd European Study Group Mathematics with Industry. ed. / J. Frank; R. van der Mei; A. den Boer; J. Bosman; N. Bouman; S. van Dam; C. Verhoef. Amsterdam : C.W.I., 2010. p. 54-85.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

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T1 - Modeling and optimization of algae growth

AU - Thornton, Anthony Richard

AU - Weinhart, Thomas

AU - Bokhove, Onno

AU - Zhang, Bowen

AU - van der Sar, Dick M.

AU - Kumar, Kundan

AU - Pisarenco, Maxim

AU - Rudnaya, Maria

AU - Savceno, Valeriu

AU - Rademacher, Jens

AU - Zijlstra, Julia

AU - Szabelska, Alicja

AU - Zyprych, Joanna

AU - van der Schans, Martin

AU - Timperio, Vincent

AU - Veerman, Frits

PY - 2010

Y1 - 2010

N2 - The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runo water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity. The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants. With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn.

AB - The wastewater from greenhouses has a high amount of mineral contamination and an environmentally-friendly method of removal is to use algae to clean this runo water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity. The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants. With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn.

KW - METIS-274054

KW - Algae growth

KW - IR-75743

KW - EWI-19034

KW - Coupled odes

KW - Optimization

KW - Numerical solution

KW - Steady state analysis

M3 - Conference contribution

SN - not assigned

SP - 54

EP - 85

BT - Proceedings of the 72nd European Study Group Mathematics with Industry

A2 - Frank, J.

A2 - van der Mei, R.

A2 - den Boer, A.

A2 - Bosman, J.

A2 - Bouman, N.

A2 - van Dam, S.

A2 - Verhoef, C.

PB - C.W.I.

CY - Amsterdam

ER -

Thornton AR, Weinhart T, Bokhove O, Zhang B, van der Sar DM, Kumar K et al. Modeling and optimization of algae growth. In Frank J, van der Mei R, den Boer A, Bosman J, Bouman N, van Dam S, Verhoef C, editors, Proceedings of the 72nd European Study Group Mathematics with Industry. Amsterdam: C.W.I. 2010. p. 54-85