Some non-intuitive properties of serial chemostats with and without mortality

Dali-Youcef, Manel; Harmand, Jérôme; Rapaport, Alain; Sari, Tewfik

doi:10.1016/j.ifacol.2022.09.140

Cited by 2 publications

(5 citation statements)

References 10 publications

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“…The equality S out r (S in , D) = S out (S in , D) is verified for the r = 0 and r = 1, see (6). In addition, we have S in = gr 1 (D), see (20).…”

Section: The Output Substrate Concentration As a Function Of The Volu...mentioning

confidence: 66%

“…Although G 1 (S in , D, r) and G 2 (S in , D, r), given by ( 36) and ( 37), respectively, are not defined for r = 0 or r = 1, the formulas ( 38) and ( 39) allow them to be extended to r = 0 and r = 1, as was done for S out r in (6). We can write…”

Section: Biogas Flow Ratementioning

confidence: 99%

“…For more information on this issue, see Section 5.4. For biological comments on the heuristic underlying this non-intuitive behaviour, the reader is refered to [6].…”

Section: The Maximal Biogas Of the Serial Configuration Can Exceed Th...mentioning

confidence: 99%

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Performance Study of Two Serial Interconnected Chemostats with Mortality

2022

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The present work considers the model of two chemostats in series when a biomass mortality is considered in each vessel. We study the performance of the serial configuration for two different criteria which are the output substrate concentration and the biogas flow rate production, at steady state. A comparison is made with a single chemostat with the same total volume. Our techniques apply for a large class of growth functions and allow us to retrieve known results obtained when the mortality is not included in the model and the results obtained for specific growth functions in both the mathematical literature and the biological literature.In particular, we provide a complete characterization of operating conditions under which the serial configuration is more efficient than the single chemostat, i.e. the output substrate concentration of the serial configuration is smaller than that of the single chemostat or, equivalently, the biogas flow rate of the serial configuration is larger than that of the single chemostat. The study shows that the maximum biogas flow rate, relative to the dilution rate, of the series device is higher than that of the single chemostat provided that the volume of the first tank is large enough. This non-intuitive property does not occur for the model without mortality.

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“…The equality S out r (S in , D) = S out (S in , D) is verified for the r = 0 and r = 1, see (6). In addition, we have S in = gr 1 (D), see (20).…”

Section: The Output Substrate Concentration As a Function Of The Volu...mentioning

confidence: 66%

Section: Biogas Flow Ratementioning

confidence: 99%

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Performance Study of Two Serial Interconnected Chemostats with Mortality

2022

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“…there is r * ∈ (0, 1) such that for any r ∈ (r * , 1), the maximum, relative to D, of G 2 (S in , D, r) will be larger than the maximum G(S in , D). Here G 2 (S in , D, r) is the biogas flow rate of the serial configuration at steady state E 2 and G(S in , D) is the biogas flow rate of the single chemostat, see [1,3]. This result was obtained by showing that the first partial derivative in r = 1 (at left) of…”

Section: 3mentioning

confidence: 98%

“…2 , then curves Π r1 and Φ r do not intersect; if 3− √ 5 2 < r < 1 2 , then curves Π r1 and Φ r intersect at point Q 1 . Proof.…”

Section: Monod Growth Function We Consider the Monod Growth Function ...mentioning

confidence: 99%

The productivity of two serial chemostats

Dali-Youcef

Sari

2022

Int. J. Biomath.

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show abstract

Some non-intuitive properties of serial chemostats with and without mortality

Cited by 2 publications

References 10 publications

Performance Study of Two Serial Interconnected Chemostats with Mortality

Performance Study of Two Serial Interconnected Chemostats with Mortality

The productivity of two serial chemostats

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