General information
Offer title : Post-doctoral student (M/F) – IMT (Toulouse) – Modelling and data assimilation for wastewater treatment (H/F)
Reference : UMR5219-TAMAZA-012
Number of position : 1
Workplace : TOULOUSE
Date of publication : 18 September 2024
Type of Contract : FTC Scientist
Contract Period : 12 months
Expected date of employment : 1 November 2024
Proportion of work : Full time
Remuneration : between €2,991 and €4,166 gross per month depending on experience
Desired level of education : Niveau 8 – (Doctorat)
Experience required : 1 to 4 years
Section(s) CN : Mathematics and mathematical interactions
Missions
The proposal is to establish and calibrate a simplified deterministic model that describes the operation of an activated sludge wastewater treatment plant. The calibration algorithm will rely on a data assimilation strategy based on available online measured data and will routinely reconstruct unmeasured variables. The modeling will specifically describe the biological absorption and physicochemical adsorption mechanisms of phosphate, as well as other major processes occurring in the tank.
This detailed modeling will then allow the proposal of control strategies to optimize the respective contributions of biological and physicochemical phosphorus removal. The goal is to release water with the lowest possible residual phosphate concentration while ensuring a comprehensive nitrogen treatment.
Activities
The proposed approach consists of five steps.
Step 1: Model simplification
The biological operation of activated sludge can be described in detail using the internationally recognized ASM model. The full model describes the evolution of many chemical and bacterial species and requires several dozen coupled nonlinear ordinary differential equations (ODEs). However, depending on the objective, accounting for all these equations can be unnecessary and restrictive. Our approach is to select the essential equations and reduce the number of parameters.
Three possible states of the activated sludge tank will be considered:
• Aerobic: O2 present due to aeration,
• Anoxic: No O2 but NO3 is present,
• Anaerobic: No O2 nor NO3.
The mechanisms associated with these three states will focus on nitrogen treatment (nitrification and denitrification) and phosphate treatment (biological absorption and adsorption on iron hydroxides). For each state, we will propose a simplification of the mechanisms by fixing reaction constants instead of making them depend on concentrations. Additionally, quantities that vary over several weeks (such as water temperature, which influences reaction constants, and biomass quantity) will be considered constant. This simplified model will consist of linear ODEs (or fewer nonlinearities) for each regime identified. The direct simulations of this simplified model will be qualitatively compared to available measurements, helping refine which mechanisms can be simplified.
Step 2: Model calibration with experimental data
In this step, available data will be assimilated to calibrate the model’s parameters. We will rely on comprehensive measurement data obtained from an over-equipped experimental station over three years. Phosphate measurements are not routinely available, but they will be used for model development. If the model does not reproduce the data accurately, we will revisit the simplifications (Step 1) to achieve satisfactory results. Data assimilation will be done using a variational method, minimizing the L2 norm of deviations from measurements. Some sensors are not perfectly calibrated and may drift over time, so precautions will be taken, possibly adding calibration constants to the parameters to be identified. A preliminary study showed that the numerous parameters are challenging to estimate as a whole. To improve robustness, we will also include measured constants from signals, such as O2 plateau values and NH4 and NO3 rise/fall rates.
Step 3: Identifiability of NH4, NO3, PO4 concentrations
In routine operations, NH4, NO3, and PO4 concentrations are not measured. The only quantities measured are inflow rate, dissolved oxygen, and redox potential. However, for NH4 and NO3, there are moments when these chemicals disappear from the tank, as the O2 and redox profiles show detectable singular points. This allows for reliable initial conditions. For phosphorus, the phenomena are more complex: phosphorus-removing bacteria absorb phosphate under aerobic conditions, release a little during anoxic phases, and release a significant amount in anaerobic phases. Therefore, there are three reaction constants associated with PO4: aerobic phosphorus removal rate, anoxic phosphorus release rate, and anaerobic phosphorus release rate. We will explore how the evolution of PO4 concentration can be reconstructed, at least qualitatively, and ideally quantitatively. These reconstructed variables could provide guidance for operating the installation.
Step 4: Theoretical control strategy
We will implement an optimal control strategy for aeration in the tank. First, we will assume a known and constant inflow source (volume and concentrations) over time. The optimal control will involve proposing a periodic strategy that ensures complete nitrogen removal and minimizes phosphorus levels. In a second phase, we will consider a variable inflow source and seek an optimal strategy in this context. The work from Erika Varga’s Ph.D. (2022) suggests that improving biological phosphorus removal generally requires extending total aeration time (thus increasing electricity consumption), and a balance must be found between treatment quality and energy consumption.
Step 5: Effective control strategy
In real-life situations, the inflow source is not precisely known, and the control strategy cannot rely on this information. Real-time control must adjust aerator commands based on measured O2 and redox signals.
Skills
The proposed project includes aspects of modeling, numerical computation, data assimilation, and optimal control. To successfully carry out the study, a code will need to be developed, ideally using Python.
In addition, certain mathematical concepts will be used during the project:
• Modeling phenomena using ODEs, numerical resolution of these equations – Step 1.
• Variational data assimilation. This involves calibrating a deterministic model (in this case: an ODE model) based on observations, optimizing the deviation from measurements while constrained by the ODE model – Steps 2 and 3.
• Optimal control. This involves finding the source term in a model to optimize an objective function (here: the residual amount of phosphorus and nitrogen), with mathematical tools similar to data assimilation – Steps 4 and 5.
Work Context
The CRITT GPTE of INSA Toulouse and the Toulouse Mathematics Institute (IMT) have been collaborating for four years. They have successfully developed a control algorithm to optimize nitrogen treatment and daily diagnose the basin’s status. This solution combines an innovative automation system that controls the station’s aeration system (AERATION module, Inflex automaton developed at INSA and in operation for ten years across dozens of stations) with a computation code (DIAGNOSTIC module). The approach relies on detecting singular points in oxygen and redox signals and consulting a library of correlations linking the shapes of these profiles to the progress of biological reactions. A software license has been filed for this product, which is currently being marketed by a Toulouse-based company.
The PHOSTWIN project aims to propose a control system that efficiently removes phosphorus while maintaining effective nitrogen treatment. This project is co-financed by the Adour-Garonne Water Agency (Toulouse) and AMIES (Agency for Mathematics in Interaction with Business and Society). The contract is expected to be signed by the end of 2024.
Additional Information
Benefits associated with the post: – Contribution to transport, health insurance and catering costs, – 32 days annual leave and 13 days RTT, – Possibility of teleworking, – Preferential rates for certain cultural and sports establishments, – Holiday vouchers subject to conditions.
