Multiple steady state profiles in interconnected biological systems

Dramé, Abdou Khadry; Harmand, Jérôme; Rapaport, Alain; Lobry, Claude

doi:10.1080/13873950600723277

Cited by 14 publications

(13 citation statements)

References 11 publications

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“…A biological water treatment plant is complex to operate firstly because the system is bistable [25][26][27][28] and secondly because the direct measurements about the system state can be made only rather infrequently. The bistability arises because the material to be treated is a nutrient for the microbes in small concentrations but toxic in high concentrations.…”

Section: Case 4: Managing a Biological Water Treatment Plantmentioning

confidence: 99%

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Operations’ decision making under uncertainty: case studies on papermaking

Jokinen

Konkarikoski

Pulkkinen

et al. 2009

Mathematical and Computer Modelling of Dynamical Systems

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Operational decisions are influenced not only by the data and models available to the decision maker but also by the uncertainty in the data and in model-based predictions about the impacts of decision makers' actions. In non-linear systems the potential actions may have widely differing uncertainty associated with them. Then the decision maker must take an attitude towards risk and balance that against the expectation value of performance. In stochastic optimization, methods to deal with uncertainty have been developed. However, these methods have not been widely used in decision making about operating industrial processes. In this article, we first present a short summary of decision making under uncertainty and then suggest that the mathematical structure of stochastic optimization serves as a model for the architecture of future operational decision support systems. We demonstrate this framework by analysing four idealized operational decision cases, which are closely related to practical daily decision making tasks at paper mills. However, the explicit risk analysis introduces concepts that are new to operational decision makersoperators and engineersand thus is challenging to implement in practice.

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Section: Case 4: Managing a Biological Water Treatment Plantmentioning

confidence: 99%

“…Rather than considering a detailed model [25], here we shall discuss a simple discretetime model of bistability:…”

Section: Case 4: Managing a Biological Water Treatment Plantmentioning

confidence: 99%

Operations’ decision making under uncertainty: case studies on papermaking

Jokinen

Konkarikoski

Pulkkinen

et al. 2009

Mathematical and Computer Modelling of Dynamical Systems

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“…Dramé et al [8] analysed a standard reactor cascade model, considering two abstract representations for the specific growth rate. When the specific growth rate is a monotonically increasing function, such as the Monod expression, then there is at most one no-washout steady-state solution in each reactor.…”

Section: Introductionmentioning

confidence: 99%

An Analysis of a Standard Reactor Cascade and a Step-Feed Reactor Cascade for Biological Processes Described by Monod Kinetics

Sidhu

Nelson

Balakrishnan

2015

Chemical Product and Process Modeling

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We analyse the steady-state operation of two types of reactor cascade without recycle. The first is a standard reactor cascade in which the feed stream enters into the first reactor. The second is a step-feed reactor cascade in which an equal proportion of the feed stream enters each reactor in the cascade. The reaction is assumed to be a biological process governed by Monod growth kinetics with a decay coefficient for the microorganisms. The steady-states of both models are found for an arbitrary number of reactors and their stability determined as a function of the residence time. We show that in a step-feed reactor cascade the substrate and biomass concentrations leaving the reactor of the cascade are identical to those leaving the first reactor of the cascade. We further show that this result is true for a general specific growth rate of the form μ (S,X). Thus for such processes the non-standard cascade offers no advantage over that of a single reactor. This is surprising because the use of a non-standard cascade has been proposed as a mechanism to improve the biological treatment of wastewater.

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“…For instance, it has been used to reproduce marine environment [18] or to model rhizosphere [11], and has motivated several mathematical studies [43,20,9,37,47,39,17,41,12]. Similarly, an interest for series of bioreactors appeared in biochemical industry, with tanks of possibly different volumes to be optimized [26,19,4,15,8]. Although island models have been proposed in ecology since the late sixties [27], relatively few studies have considered non-serial interconnections of chemostats [38].…”

Section: Introductionmentioning

confidence: 99%