Parameter identification of Droop model: an experimental case study

Benavides, Micaela; Hantson, Anne-Lise; Impe, Jan Van; Wouwer, Alain Vande

doi:10.1007/s00449-015-1419-2

Cited by 14 publications

(9 citation statements)

References 14 publications

(16 reference statements)

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“…Notably, the value ofv 1 only includes the zc 0 parameter for the value of z in the stationary state, which means that changes in this parameter result in a change in the equilibrium pointv 1 of the system and, particularly of interest, in the amount of biomass (Figure 3). The parameters and initial conditions were obtained from [48]. Additionally, the bifurcation diagram of the state variable y is illustrated in Figure 4.…”

Section: Finding the Stability Of The Absence Of Biomass Equilibriummentioning

confidence: 99%

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Sensitivity, Equilibria, and Lyapunov Stability Analysis in Droop’s Nonlinear Differential Equation System for Batch Operation Mode of Microalgae Culture Systems

et al. 2021

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Microalgae-based biomass has been extensively studied because of its potential to produce several important biochemicals, such as lipids, proteins, carbohydrates, and pigments, for the manufacturing of value-added products, such as vitamins, bioactive compounds, and antioxidants, as well as for its applications in carbon dioxide sequestration, amongst others. There is also increasing interest in microalgae as renewable feedstock for biofuel production, inspiring a new focus on future biorefineries. This paper is dedicated to an in-depth analysis of the equilibria, stability, and sensitivity of a microalgal growth model developed by Droop (1974) for nutrient-limited batch cultivation. Two equilibrium points were found: the long-term biomass production equilibrium was found to be stable, whereas the equilibrium in the absence of biomass was found to be unstable. Simulations of estimated parameters and initial conditions using literature data were performed to relate the found results to a physical context. In conclusion, an examination of the found equilibria showed that the system does not have isolated fixed points but rather has an infinite number of equilibria, depending on the values of the minimal cell quota and initial conditions of the state variables of the model. The numerical solutions of the sensitivity functions indicate that the model outputs were more sensitive, in particular, to variations in the parameters of the half saturation constant and minimal cell quota than to variations in the maximum inorganic nutrient absorption rate and maximum growth rate.

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Section: Finding the Stability Of The Absence Of Biomass Equilibriummentioning

confidence: 99%

“…The estimated growth parameters for the two predictions were the same except for the initial conditions. The experimental setup and parameter estimation can be found in [48]. It is important to remark upon how the equilibria changed under initial conditions, although the same parameters were used (Figures 6 and 7).…”

Section: Simulations Of the Modelmentioning

confidence: 99%

Sensitivity, Equilibria, and Lyapunov Stability Analysis in Droop’s Nonlinear Differential Equation System for Batch Operation Mode of Microalgae Culture Systems

et al. 2021

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“…Figure 1 illustrates some of the most common variables involved in a microalgae photobioreactor, either as inputs or outputs. An example of this kind of model can be found in [18], where a parameter identification is performed over batch cultures of Dunaliella tertiolecta strain. In addition, modeling of neutral lipids and carbohydrates quotas were introduced in [19] with a five-state model.…”

Section: Introductionmentioning

confidence: 99%

Experimental Study of Substrate Limitation and Light Acclimation in Cultures of the Microalgae Scenedesmus obliquus—Parameter Identification and Model Predictive Control

et al. 2020

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In this study, the parameters of a dynamic model of cultures of the microalgae Scenedesmus obliquus are estimated from datasets collected in batch photobioreactors operated with various initial conditions and light illumination conditions. Measurements of biomass, nitrogen quota, bulk substrate concentration, as well as chlorophyll concentration are achieved, which allow the determination of parameters with satisfactory confidence intervals and model cross-validation against independent data. The dynamic model is then used as a predictor in a nonlinear model predictive control strategy where the dilution rate and the incident light intensity are simultaneously manipulated in order to optimize the cumulated algal biomass production.

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“…A mathematical model is a tool to envision phenomena logically. A differential equation is a type of the model which is commonly used in microorganism research, for instance, microalgae and bacteria [3,10,22]. This field of research has a high impact on innovative works because of the products of the cells [16,19,21] and to environmental and watery ecological studies [9,12,18,26,29].…”

Section: Introductionmentioning

confidence: 99%

“…For the Droop model, the change of growth of the organisms can be described and predicted by changing the substrate concentration made by those organisms and the dilution. Its growth rate depends on the cell quota for the nutrient, which is the nutrient usage, and the change of cell quota depends on the focused nutrient in the supply [3]. For the logistic model, its growth rate is a constant and the growth is bounded by the environmental term [2].…”

Section: Introductionmentioning

confidence: 99%

A Novel Droop-Logistic Model for Microorganism Population Studies

Thongthaisong

Triampo

Amornsamankul

2018

International Journal of Simulation: Systems, Science &Amp; Technology

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In this work the Droop model and logistic model are combined to form another mathematical model for a microorganism population that is named the Droop-Logistic model. The equation of the organism growth of this model is from the logistic model, and the growth rate is from the Droop model. Our new model is shown to have a unique solution on an open set by the Lipschitz condition. By analyzing local stability, the condition for having maximum cell numbers and the condition for being stable from the balancing of the surrounding nutrient and the intracellular quota are determined. Numerical examples are given three values of dilution rate. It was found that when the dilution rate satisfies the condition of maximum growth, i.e. it is less than the maximum growth rate, then the cell number will reach its maximum at the stationary time. If the dilution rate is greater than the maximum growth rate, then the cell number will decrease to zero. Lastly, if the dilution rate is zero and the maximum growth condition is satisfied, then the cell number will tend to the maximum value as well.

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Parameter identification of Droop model: an experimental case study

Cited by 14 publications

References 14 publications

Sensitivity, Equilibria, and Lyapunov Stability Analysis in Droop’s Nonlinear Differential Equation System for Batch Operation Mode of Microalgae Culture Systems

Sensitivity, Equilibria, and Lyapunov Stability Analysis in Droop’s Nonlinear Differential Equation System for Batch Operation Mode of Microalgae Culture Systems

Experimental Study of Substrate Limitation and Light Acclimation in Cultures of the Microalgae Scenedesmus obliquus—Parameter Identification and Model Predictive Control

A Novel Droop-Logistic Model for Microorganism Population Studies

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