Réduction du modèle ASM 1 pour la commande optimale des petites stations d'épuration à boues activées

L'adoption par l'Union Européenne de normes de rejets plus contraignantes implique une meilleure gestion des stations d'épuration. L'utilisation de modèles de simulation dynamique dans des schémas de commande en boucle fermée constitue une alternative intéressante pour répondre à ce problème.Sur la base du modèle ASM 1, un modèle réduit est ici élaboré pour le procédé à boues activées en aération séquentielle, en vue de la commande optimale du système d'aération. Les simplifications considérées sont de deux types : (i) les dynamiques lentes du système sont identifiées au moyen d'une méthode d'homotopie, puis éliminées du modèle ; (ii) des simplifications plus heuristiques consistant à prendre en compte un composé organique unique et à éliminer la concentration des composés organiques azotés sont ensuite appliquées. Elles conduisent à un modèle simplifié de 5 variables. L'application d'une procédure d'identification paramétrique permet alors de démontrer que le comportement dynamique du modèle simplifié est en bonne adéquation avec celui du modèle ASM 1 sur un horizon de prédiction de plusieurs heures, même lorsque les concentrations de l'influent ne sont pas connues. Il est également vérifié que le modèle proposé est observable et structurellement identifiable, sous des conditions d'aérobiose et d'anoxie, à partir des mesures en ligne des concentrations en oxygène dissous, ammoniaque et nitrate.Le modèle simplifié développé présente ainsi toutes les propriétés requises pour une future utilisation au sein de schémas de commande en boucle fermée, en vue de la commande optimale des petites stations d'épuration à boues activées.In order to meet the stricter wastewater effluent guidelines adopted by the European Union, wastewater treatment plants require better management strategies. Wastewater treatment process models have become a major tool to design closed-loop control schemes. However, the dynamic models that are currently used in the simulation of activated sludge treatment plants (ASM 1, ASM 2 and, more recently, ASM 3 models) are highly dimensional and are not appropriate for on-line implementation (e.g., for model predictive control or optimal control). It is therefore important to develop reduced models that could be used for this purpose.A reduced model was developed to describe the behaviour of alternating activated sludge treatment plants, with the aim of applying it to the optimal control of an aeration system. The reduction scheme was based on appropriate simplifications to the ASM 1 model (which is more appropriate for open-loop control). The objective was to verify if accurate predictions could be made time periods of several hours (about 8 h).The present results are related to an existing small-size wastewater treatment plant. This plant was designed for 15,000 population-equivalents (p.e.) and consists of a primary treatment stage (screening, grit removal, primary sedimentation), followed by a secondary treatment stage (biological treatment). The latter consists of a single aeration tank of about 2,050 m3 equipped with 3 turbines which are operated cyclically to create alternating aerobic and anoxic conditions. Ammonia is converted into nitrate during air-on periods (nitrification step) and nitrate is subsequently removed during air-off periods (denitrification step). It is important to note that a dynamic model, based on the ASM 1 model and calibrated from a set of input/output measurements over a one-day period (Chachuat, 2001), was used here as a reference to perform model reduction. The following two-level simplification procedure was applied :· A homotopy method was first used to establish relationships between the states and the dynamics of the system, via an eigenvalue decomposition. The components that are associated with the slowest dynamics are then assumed constant to reduce the state space dimension. Heterotrophic (XB,H) and autotrophic (XB,A) biomass and inert particulate organic compounds (XI) were detected as the slow state variables. It was found that the short-term predictions of the dynamic model were not affected by assuming that XI, XB,H and XB,A concentrations were constant. Eliminating these 3 state variables, along with the concentrations of soluble inert organic compounds (SI), resulted in a 7-dimensional dynamic model.· However, further simplifications were required to enable the on-line optimisation of the bioreactor aeration profiles with reasonable computational times. These simplifications consisted of taking into account the process specifications in order to reduce the state space dimension to 4 or 5, and were therefore based on more heuristic considerations. Both organic and nitrogenous compounds are under consideration: (i) a single organic compound (denoted as XDCO) is formed by adding soluble and particulate organic compound concentrations, and (ii) the mathematical expression that describes the organic nitrogen hydrolysis process is simplified so that the dynamics with respect to soluble and particulate organic nitrogen are independent.The two previous simplification steps produced a reduced 5-dimensional dynamic model with state variables XDCO, SNO, SNH, SND and SO. It should also be noted that the resulting model involved the parameters YH, iNBM, KS, KNO, KO,H, KNH,A, ηNO,g and ηNO,h that are identical to those defined in the original ASM 1 model by Henze et al. (1987). In addition, 7 specific parameters were defined defined (θ1, θ2, θ3, θ4, θ5, KDCO, KND). These new parameters exhibited rather slow temporal variation, thus agreeing with the general ASM 1 model for short time periods.Afterwards, a two-step procedure was applied to calibrate the model. This procedure first consisted of determining a reduced set of identifiable parameters by the use of both sensitivity and principal component analyses. Note that the inlet concentrations of organic compounds, ammonia nitrogen and soluble organic nitrogen may be considered as additional parameters since they are generally not measured on-line. The selected parameters (θ1, θ2, θ3) and inlet concentrations (XinDCO, SinNH) were then estimated by the application of a local gradient search method (successive quadratic programming, SQP). Comparisons between the dynamic behaviour of both reduced and ASM 1 models show that accurate predictions can be obtained over time periods of several hours (8 h). It was also shown that the reduced model was observable and structurally identifiable under aerobic and anoxic conditions from dissolved oxygen, ammonia and nitrate concentration measurements. These results therefore demonstrate the ability of the reduced model to be embedded into closed-loop control schemes.The conclusions from this work are twofold: (i) The reduced model can be used as a basis to construct an on-line observer to estimate the unmeasured state variables, the unknown (most sensitive) parameters and inlet concentrations; (ii) Non-linear model predictive control (NMPC) schemes can then be implemented to operate the aeration system so that the nitrogen discharge or the energy consumption are minimised (optimal control).The initial results demonstrate that the application of NMPC strategies is likely to give large reductions of nitrogen discharge with respect to usual operating strategies (e.g., oxygen or redox control). Such closed-loop control schemes are particularly efficient in dealing with large influent variations (inlet flow rate, concentration and composition) resulting from both human activities and climatic conditions, and inherent modelling uncertainties. However, an experimental validation of this control strategy on a pilot scale or an industrial scale is required to confirm these results

Dynamic coupling of photoacclimation and photoinhibition in a model of microalgae growth.

International audienceThe development of mathematical models that can predict photosynthetic productivity of microalgae under transient conditions is crucial for enhancing large-scale industrial culturing systems. Particularly important in outdoor culture systems, where the light irradiance varies greatly, are the processes of photoinhibition and photoacclimation, which can affect photoproduction significantly. The former is caused by an excess of light and occurs on a fast time scale of minutes, whereas the latter results from the adjustment of the light harvesting capacity to the incoming irradiance and takes place on a slow time scale of days. In this paper, we develop a dynamic model of microalgae growth that simultaneously accounts for the processes of photoinhibition and photoacclimation, thereby spanning multiple time scales. The properties of the model are analyzed in connection to PI-response curves, under a quasi steady-state assumption for the slow processes and by neglecting the fast dynamics. For validation purposes, the model is calibrated and compared against multiple experimental data sets from the literature for several species. The results show that the model can describe the difference in photosynthetic unit acclimation strategies between Dunaliella tertiolecta (n-strategy) and Skeletonema costatum (s-strategy)

A model of chlorophyll fluorescence in microalgae integrating photoproduction, photoinhibition and photoregulation

This paper presents a mathematical model capable of quantitative prediction of the state of the photosynthetic apparatus of microalgae in terms of their open, closed and damaged reaction centers under variable light conditions. This model combines the processes of photoproduction and photoinhibition in the Han model with a novel mathematical representation of photoprotective mechanisms, including qE-quenching and qI-quenching. For calibration and validation purposes, the model can be used to simulate fluorescence fluxes, such as those measured in PAM fluorometry, as well as classical fluorescence indexes. A calibration is carried out for the microalga Nannochloropsis gaditana, whereby 9 out of the 13 model parameters are estimated with good statistical significance using the realized, minimal and maximal fluorescence fluxes measured from a typical PAM protocol. The model is further validated by considering a more challenging PAM protocol alternating periods of intense light and dark, showing a good ability to provide quantitative predictions of the fluorescence fluxes even though it was calibrated for a different and somewhat simpler PAM protocol. A promising application of the model is for the prediction of PI-response curves based on PAM fluorometry, together with the long-term prospect of combining it with hydrodynamic and light attenuation models for high-fidelity simulation and optimization of full-scale microalgae production systems

Global sensitivity analysis in life-cycle assessment of early-stage technology using detailed process simulation: application to dialkylimidazolium ionic liquid production.

The ability to assess the environmental performance of early-stage technologies at production scale is critical for sustainable process development. This paper presents a systematic methodology for uncertainty quantification in life-cycle assessment (LCA) of such technologies using global sensitivity analysis (GSA) coupled with a detailed process simulator and LCA database. This methodology accounts for uncertainty in both the background and foreground life-cycle inventories, and is enabled by lumping multiple background flows, either downstream or upstream of the foreground processes, in order to reduce the number of factors in the sensitivity analysis. A case study comparing the life-cycle impacts of two dialkylimidazolium ionic liquids is conducted to illustrate the methodology. Failure to account for the foreground process uncertainty alongside the background uncertainty is shown to underestimate the predicted variance of the end-point environmental impacts by a factor of two. Variance-based GSA furthermore reveals that only few foreground and background uncertain parameters contribute significantly to the total variance in the end-point environmental impacts. As well as emphasizing the need to account for foreground uncertainties in LCA of early-stage technologies, these results illustrate how GSA can empower more reliable decision-making in LCA

A pathway towards net-zero emissions in oil refineries

Rapid industrialization and urbanization have increased the demand for both energy and mobility services across the globe, with accompanying increases in greenhouse gas emissions. This short paper analyzes strategic measures for the abatement of CO2 emissions from oil refinery operations. A case study involving a large conversion refinery shows that the use of post-combustion carbon capture and storage (CCS) may only be practical for large combined emission point sources, leaving about 30% of site-wide emissions unaddressed. A combination of post-combustion CCS with a CO2 capture rate well above 90% and other mitigation measures such as fuel substitution and emission offsets is needed to transition towards carbon-neutral refinery operations. All of these technologies must be configured to minimize environmental burden shifting and scope 2 emissions, whilst doing so cost-effectively to improve energy access and affordability. In the long run, scope 3 emissions from the combustion of refinery products and flaring must also be addressed. The use of synthetic fuels and alternative feedstocks such as liquefied plastic waste, instead of crude oil, could present a growth opportunity in a circular carbon economy

A Dual Modifier-Adaptation Approach for Real-Time Optimization

For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable plant-model mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach does not require the model parameters to be estimated on-line. Instead, it uses information regarding the constraints and selected gradients to improve the plant operation. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the norm of the gradient errors, which is used as a constraint when determining the next operating point. The proposed approach is demonstrated via numerical simulation for both an unconstrained and a constrained problem

Exploration of trade-offs between steady-state and dynamic properties in signaling cycles

In the intracellular signaling networks that regulate important cell processes, the base pattern comprises the cycle of reversible phosphorylation of a protein, catalyzed by kinases and opposing phosphatases. Mathematical modeling and analysis have been used for gaining a better understanding of their functions and to capture the rules governing system behavior. Since biochemical parameters in signaling pathways are not easily accessible experimentally, it is necessary to explore possibilities for both steady-state and dynamic responses in these systems. While a number of studies have focused on analyzing these properties separately, it is necessary to take into account both of these responses simultaneously in order to be able to interpret a broader range of phenotypes. This paper investigates the trade-offs between optimal characteristics of both steady-state and dynamic responses. Following an inverse sensitivity analysis approach, we use systematic optimization methods to find the biochemical and biophysical parameters that simultaneously achieve optimal steady-state and dynamic performance. Remarkably, we find that even a single covalent modification cycle can simultaneously and robustly achieve high ultrasensitivity, high amplification and rapid signal transduction. We also find that the response rise and decay times can be modulated independently by varying the activating- and deactivating-enzyme-to-interconvertible-protein ratios

Sensitivity analysis of uncertain dynamic systems using set-valued integration

We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York