Universit´ e Cˆ ote d’Azur, Inria, INRAE, CNRS, Sorbonne Universit´ e Biocore team, Sophia Antipolis, France
February 3, 2021
Abstract Fast growing E. coli cells in glucose-aerobic conditions excrete fer- mentation by-products such as acetate. This phenomenon is known as overflow metabolism and can pose a major problem in industrial bio-processes. In this paper, we study optimal control strategies for feeding a fed-batchreactor subject to overflow metabolism. We consider that acetate has an inhibitor effect on the glucose uptake, and we also consider the cost associated to process duration. In our approach, using the Pontryagin Maximum Principle and numerical solutions we describe the optimal feeding policy that maximizes biomass productivity and minimizes the cost duration of the process. We show that a singular regime is possible, in which cells grow at a slow rate to prevent acetate formation. If the cost associated to the process is too high, only bang-bang solutions are allowed. keywords: Dynamics and control; Industrial biotechnology; Fed-batch; Over- flow metabolism
Even though the different MPC approaches presented above gave satisfactory results for batchreactor control than conven- tional PID controllers, they also involve the resolution of a quadratic problem (QP). The computational burden associated with solving an on-line QP can be heavy and may require a standalone computer. In the last decade a predictive functional control (PFC) technique has been pioneered (Richalet, 1993). The advantage of PFC compared to the different MPC con- figurations is its flexibility to transform a QP problem into a square system of equations, which allows for an easier imple- mentation in practice. Also PFC is distinct from other MPC implementations in several ways: the SISO version, uses refer- ence trajectories, coincidence points and can be applied to the control of a linear or non-linear process without need of model linearization (Badgwell & Qin, 2001). PFC is very open and can integrate a number of concepts resulting from other approaches. It can be implemented in simple industrial automats but also in numerical systems of centralized control (NSCC) or industrial PCs (Richalet, Lavilelle, & Mallet, 2004). The PFC technique handles systems with varying dynamics, with or without inte- grator, with stable or unstable open loop, with or without dead time, and, generally systems that are difficult to control with a classical PID. The attractive features of PFC are:
The current practice in the chemical industry involves the use of optimal techniques based on experimental planning (Box et al., 1978). These methods do not attempt to determine a mechanistic interpretation of the transformation. They make use of an input-output model; although yielding good results in many cases, they do not allow one to incorporate any existing understanding of the transform- ation and thus all the information gained from the experience of chemists goes unused. Moreover, any change in the criterion or in the experimental factors induces one to repeat the whole procedure, resulting in an additional and expensive experi- mental effort. The numerical problem of batchreactor performance optimization has attracted a lot of attention (Bonvin, 1998); numerous numerical optimization tech- niques are available in the literature (Edgar and Himmelblau, 1988). The optimal temperature profile or the optimal feed rate profile has been determined for simple reaction networks and for several criteria such as the maximal concentration of a desired product (Rippin, 1983). Several types of objective functions can be readily studied at low cost, but these tools require an accurate model of the process under consideration. Since fine chemical reactions are usually complex, their kinetics are poorly known. Classical kinetic studies are not possible because they are time- consuming in comparison with the duration of the marketing campaigns and the economic objectives.
4. Transposition from semi-batch to
continuous process: impact on safety
4.1. Nitration of toluene in semi-batch process
In order to control the temperature rise due to the exother- micity of the reaction, the nitration of toluene is generally carried out in a fed batch (semi-batch) reactor. The reactor is initially filled with toluene and the acid mixture is fed. The total operation time is between 2 and 4 h. It takes into account the feeding time of the acid mixture, around 1.5–3 h ( Rusli et al., 2013; D’Angelo et al., 2003 ). D’Angelo et al. (2003) car- ried out the reaction at a laboratory scale in a jacketed reactor of 1.5 L where the monofluid is a glycol–water mixture. The experimental setup is given in Fig. 4 . The monofluid temper- ature is controlled using a heating–cooling system composed of an electrical resistance and two plate heat-exchangers (the first one uses water at 15 ◦ C, the second one a glycol–water mixture at − 10 ◦ C). The operating conditions are described in
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E-mail address: Philippe.Evon@ensiacet.fr (Ph. Evon, corresponding author)
Aqueous extraction process is an alternative to the solvent oil extraction process from oilseeds. It enables simultaneous recovery of oil and protein. Water extraction of sunflower oil is carried out with a mixer (model Waring Blendor, USA) as batchreactor (seeds/water: 15/85). This only apparatus carries out two essential unit operations: conditioning and grinding of sunflower seeds and liquid/solid extraction. However, lixiviation of kernels is incomplete.
This paper proposes to re-visit the problem of gas-liquid crystallization in the framework of a two-layer model and with the help of data coming from experiments on methane hydrate crystallization in a semi-batchreactor. Preliminary quantitative discussion of the order of magnitude of different effects makes possible realistic simplifications in the theoretical models. In particular, the role of the interfacial film is clearly defined. As previous authors did, we use a formulation in terms of moments of the crystal size distribution, however we are not interested in the numerical solution to the corresponding differential system, but we propose a general procedure to express analytically the asymptotic behaviour of the physical system. Thanks to this formulation, influence of different parameters can be easily identified and validated on available experimental data.
A B S T R A C T
The relevant microorganims driving e ﬃciency changes in anaerobic digestion of phenol remains uncertain. In this study correlations were established between microbial population and the process performance in an anaerobic sequencing batchreactor (ASBR) treating increasing concentrations of phenol (from 120 to 1200 mg L −1 ). Sludge samples were taken at di ﬀerent operational stages and microbial community dynamics was ana- lyzed by 16S rRNA sequencing. In addition, bamA gene was quanti ﬁed in order to evaluate the dynamics of anaerobic aromatic degraders. The microbial community was dominated by Anaerolineae, Bacteroidia, Clostridia, and Methanobacteria classes. Correlation analysis between bamA gene copy number and phenol concentration were highly signi ﬁcant, suggesting that the increase of aromatic degraders targeted by bamA assay was due to an increase in the amount of phenol degraded over time. The incremental phenol concentration aﬀected hydro- genotrophic archaea triggering a linear decrease of Methanobacterium and the growth of Methanobrevibacter. The best performance in the reactor was at 800 mg L −1 of phenol. At this stage, the highest relative abundances of Syntrophorhabdus, Chloroﬂexus, Smithella, Methanolinea and Methanosaeta were observed and correlated posi- tively with initial degradation rate, suggesting that these microorganisms are relevant players to maintain a good performance in the ASBR.
CNRS, Laboratoire de Ge´nie Chimique, INP, UMR 5503, 4 alle´e Emile Monso BP 84234, F-31432 Toulouse Cedex 4, France
a b s t r a c t
Calcium phosphate precipitation inside microbial granules cultivated in a granular sequenced batchreactor (GSBR) has been demonstrated to contribute to phosphorus removal during wastewater treatment. Whereas hydroxyapatite (HAP) is proven to accumulate in the granule, the main calcium phosphate precursors that form prior to HAP are here investigated. A separate batchreactor was used to distinguish reactions involving biological phosphate removal from physicochemical reactions involving phosphate precipitation in order to establish the kinetics and stoichiometry of calcium phosphate formation. Experiments and simulations with PHREEQC and AQUASIM software support the assump- tion that amorphous calcium phosphate (ACP) is the intermediary in HAP crystallization. The results provide the kinetic rate constants and thermodynamic constants of ACP. The formation of bioliths inside biological aggregates as well as the main parameters that drive their formations are discussed here. Finally, the inﬂuence of pH and calcium and phosphate concentrations in the inﬂuent was also assessed, in order to determine the contribution of precipitation in the different operating conditions.
This paper deals with the observability singularity problem of batch bioreactors on the positive Orthant. This singularity is overcame by the dedicated approach
based on the well-known high order sliding mode dif- ferentiator proposed by Arie Levant and the resolution of simple second order equation. Nevertheless, it is dif- ficult to distinguish between both solutions, but the sec- ond differentiation of the output gives an appropriate test procedure for choice between both solutions. Some simulation results highlight the well-founded of the pro- posed method.
gypsum and hemihydrate are 2 305 and 2 766 kg/m 3 . This weak difference between densities cannot account for the significant difference between the mean diameters of initial and final powders (see Figure 3): the particles number is not constant, which is consistent with the mechanism assumed. From the solubility data for gypsum and HH, found in the databank of the software CHESS  beyond a given temperature, gypsum becomes more soluble than solid HH, and the crystallization of HH makes the dissolution of gypsum possible (Figure 1). The model thereafter aims to evaluate several assumptions on the dissolution, nucleation and growth processes, the corresponding kinetic expressions, and to fit their parameters using the kinetic results obtained during batch experiments. The mass distribution of initial gypsum particles is divided into classes of size L between 0.8 and 120 µm: each class i contains a mass fraction given by preliminary size analysis (Figure 2). The model takes into consideration the instantaneous dissolution rate of each class. It provides the variation of the moments of the density function of crystallizing particles, via usual relations deduced from the population balance .
4.3.4. Experimental results
To complete the theoretical study based on simulations, exper- iments are carried out to investigate the behavior of the intensified SiC HEX reactor in faulty mode. The nitration of toluene is carried out under normal operating conditions (see Section 3.3 ) at 28 ◦ C with an input acid strength of 80% until voluntary failures are caused on the utility fluid line while the process fluid circulates normally. Two failures are studied: (i) LESS utility flow rate by decreasing it from 80 L h − 1 to 20 L h − 1 followed by (ii) NO utility flow rate. Fig. 7 presents the evolution of the temperature of the process fluid all along the reactor during the failures. It appears that the temperatures stabilize 300 s after the utility flow rate reduction. The mean tempera- ture in the reactor has increased of about 1 ◦ C. During normal conditions, the reactor temperature is controlled by the utility temperature, around 28 ◦ C. This temperature is almost con- stant because of high flow rate condition. The temperature at the inlet of the reactor TI1 is slightly higher because the kinetic rate is maximal due to high concentrations of the reactants (hot spot).
Acclimated activated sludge was examined for its ability to degrade malathion with and without the presence of glucose as a potential cometabolite substrate. In this study, a packed- bed reactor (PBR) using three kinds of biofilm carriers was employed for efficient degradation of malathion. The results obtained indicate that microorganisms tested were able to degrade malathion. The observed degradation rate of the pesticide in the presence of glucose was the same as without glucose. The activated sludge was found to be able to use malathion as the sole phosphorus source. In contrast, the degradation ability of the activated sludge was lost when the pesticide was used as the sole source of sulfur. The degradation capacity of the PBR was higher than the performance obtained with the batchreactor. The reactor packed with crushed olive kernels exhibited the best performance, allowing a total removal of malathion
ABSTRACT Acclimated activated sludge was examined for its ability to de-
grade malathion with and without the presence of glucose as a potential cometabolite substrate. In this study, a packed-bed reactor (PBR) using three kinds of biofilm carriers was employed for efficient degradation of malathion. The results obtained indicate that microorganisms tested were able to degrade malathion. The observed degradation rate of the pesticide in the presence of glucose was the same as without glucose. The activated sludge was found to be able to use malathion as the sole phosphorus source. In contrast, the degra- dation ability of the activated sludge was lost when the pesticide was used as the sole source of sulfur. The degradation capacity of the PBR was higher than the performance obtained with the batchreactor. The reactor packed with crushed olive kernels exhibited the best performance, allowing a total removal of malathion (10 mg/dm 3 ) within 12 h.
Predictions not only based on stochastic approaches, but also on phenomenological theories, could provide an additional element
for governments and associations to make decision processes stronger and more robust. The idea of comparing infection dynam- ics to batchreactor behavior and chemical kinetics seems to pro- vide good information also in early stages, when the infection is progressing fast. By definition, decision-making robustness in emergencies means also to adopt more different tools for future predictions and more sophisticated models can be proposed to improve the prediction reliability. Platform and database for SARS-CoV-2 predictions and, in general, for pandemic predictions, has been launched at CMIC Dept. ‘‘Giulio Natta” Politecnico di Milano website with the aim of studying kinetic parameters for infection outbreak, transmission, mitigation and extinction.
Grubaugh et al., 2019; Joseph T. Wu et al., 2020a,b ). Moreover,
when the starting population is fixed, as it is the case during gov- ernmental lockdown, the chemical reactor mainly behaves as a
batch process, where inlet and outlet flows are null. This latter case fits appropriately the current situation in many countries and regions and the batchreactor balances can reasonably predict the infection behavior. At the end of the infection, recovered people are supposed to be immunized. If future evidences will not confirm any immunization ( Gretchen, n.d.; Jiang, 2020 ), recovered people will have to be considered reintegrated as part of the healthy pop- ulation again with the same original probability to be re-infected by the SARS-CoV-2. The kinetic mechanism will be then furtherly simplified to:
Keywords: Algorithmics, Batch Scheduling
In several communication systems messages are to be transmitted in a single hop from senders to receivers through direct connections established by an underlying switching network. In such a system, a sender (resp. receiver) cannot send (resp. receive) more than one messages at a time, while the transmission of messages between different senders and receivers can take place simultaneously. The scheduler of such a system establishes successive configurations of the switching network, each one routing a non-conflicting subset of the messages from senders to receivers. Given the transmission time of each message, the transmission time of each configuration equals to the heaviest message transmitted. The aim of the scheduler is to find a sequence of configurations such that all the messages to be finally transmitted and the total transmission time to be minimized.
This work deals with the multicriteria cost-environment design of multiproduct batch plants, where the design variables are the equipment item sizes as well as the operating conditions. The case study is a multiproduct batch plant for the production of four recombinant proteins. Given the important combinatorial aspect of the problem, the approach used consists in coupling a stochastic algorithm, indeed a Genetic Algorithm (GA) with a Discrete Event Simulator (DES). To take into account the conflicting situations that may be encountered at the earliest stage of batch plant design, i.e. compromise situations between cost and environmental considerations, a Multicriteria Genetic Algorithm (MUGA) was developed with a Pareto optimal ranking method. The results show how the methodology can be used to find a range of trade-off solutions for optimizing batch plant design.