Patrice Chatellier

Modified Anaerobic Digestion Model No.1 for dry and semi-dry anaerobic digestion of solid organic waste.

The role of total solids (TS) content in anaerobic digestion of selected complex organic matter, e.g. rice straw and food waste, was investigated. A range of TS from wet (4.5%) to dry (23%) was evaluated. A modified version of the Anaerobic Digestion Model No.1 for a complex organic substrate is proposed to take into account the effect of the TS content on anaerobic digestion. A linear function that correlates the kinetic constants of three specific processes (i.e. disintegration, acetate and propionate up-take) was included in the model. Results of biomethanation and volatile fatty acids production tests were used to calibrate the proposed model. Model simulations showed a good agreement between numerical and observed data.

Hydrodynamic Mathematical Modelling of Aerobic Plug Flow and Nonideal Flow Reactors: A Critical and Historical Review

Existing mathematical models of wastewater treatment plants focus primarily on the bioconversion processes and often do not cope with the reactor hydrodynamics. However, in the literature several aerobic plug flow bioreactors with both kinetics modelling and hydrodynamics description are reported. The authors review mathematical models of aerobic plug flow reactors, such as activated sludge reactors, fluidized bed reactors, biofilters, and trickling filters focusing on their hydrodynamic approach and on the role of the reactor configuration on the process performance. For each reactor type the following modelling approach is compared: (a) ideal model, such as plug flow or complete mixed, (b) tank in series model, (c) dispersion model and (d) computational fluid dynamic model.

Sensitivity of inverse advection–diffusion–reaction to sensor and control: A low computational cost tool

A two-dimensional (2D) concentration field may be reconstructed using inverse advection–diffusion–reaction based on pointwise sensor outputs. The studied reconstruction process consists in defining fictitious boundaries and identifying the optimal concentrations on these boundaries that minimize the data misfit. The minimization is performed by means of the adjoint method. The reconstruction process is observed to fail for some sets of sensor placements. Therefore, in this paper, we aim to develop a low computational cost framework that can be used to identify badly placed sensors and to reveal potentially optimal sensor placement. From this framework, we have derived a sensitivity tool that can predict, for a given set of sensors, which boundary concentrations are easy or difficult to identify using the inverse method. This tool only requires the resolution of an adjoint problem. It is compared with the sensitivity-to-observation method in a 2D water pipe junction with 2000 Reynolds number and 1000 Peclet number. The compared methods do produce similar quantitative and qualitative results.

Inverse Computational Fluid Dynamics: Influence of Discretization and Model Errors on Flows in Water Network Including Junctions

We present a specific inverse technique to reconstruct water pipe flows from sensor outputs. The spatial shape of the boundary velocities are chosen according to spatial velocity profiles in water pipes that conform the engineering literature. Only the time evolution of the boundary velocity has to be determined using the inverse technique. Thus, few sensors are required to reconstruct a two- or three-dimensional water pipes flow. The methodology is illustrated for three flow models: Stokes, unsteady Stokes and Navier-Stokes. To reduce the computation cost of the reconstruction, simple flow models and coarse discretisations may be employed. Nevertheless this leads to less accurate results. The present paper evaluates the influence of the flow modelling and of the dicretisation on the quality of the reconstructed velocity on two examples: a water pipe junction and a 200 m subsection from a French water network. In the water pipe junction at a 100 Reynolds number, we show that a hybrid approach combining an unsteady Stokes reconstruction and a single direct Navier-Stokes simulation outperforms the algorithms based on a single model. In the network subsection we obtain an L2 error less than 1% between the reference velocity based on Navier-Stokes equations (100 Reynolds number) and the velocity reconstructed from Stokes equation. In this case, the reconstruction lasts less than one minute. Essentially Stokes based reconstruction of a Navier-Stokes flow in junctions at Reynolds number up to 100 yields the same accuracy and proves fast.

Current Views on Hydrodynamic Models of Nonideal Flow Anaerobic Reactors

A critical review of the different hydrodynamic mathematical models available for nonideal flow configurations of both low-rate and high-rate anaerobic reactors is presented, including upflow anaerobic sludge blanket reactors, anaerobic fluidized bed reactors, anaerobic biofilters, wet and dry digesters. The review highlights the role of mathematical modeling on design and operational optimization of organic waste and wastewater treatment plants. For each reactor configuration the following approaches, proposed by various authors, are presented and compared: (a) plug flow model, (b) tank in series model, (c) dispersion model, and (d) computational fluid dynamic model. The review gives a general overview on mathematical modeling of anaerobic nonideal plug-flow reactors and compares different models indicating the advantages and disadvantages to apply them for different reactor type.

Impacts of Discretization Error, Flow Modeling Error, and Measurement Noise on Inverse Transport-Diffusion-Reaction in a T-Junction

By combining a physical model and sensor outputs in an inverse transport-diffusion-reaction strategy, an accurate cartography of the concentration field may be obtained. The paper addresses the influence of discretization errors, flow uncertainties and measurement noise on the reconstruction process of the concentration field. We consider a key element of a drinking water network that is a pipe junction where Reynolds and Peclet numbers are approximately 2000 and 1000 respectively. We show that a 10% error between the reference concentration field and the reconstructed concentration field may be obtained using a coarse discretization. Nevertheless, to keep the error below 10%, a fine concentration discretization is required. The study also details the influence of the flow approximation on the concentration reconstruction process. The flow modeling error obtained when the exact Navier-Stokes flow is approximated by a Stokes flow may lead to a 40% error in the reconstructed concentration. However if the flow field is obtained from the full set of Navier-Stokes equations, we show that the error may be less than 5%. Then, we observe that the quality of the reconstructed concentration field obtained with the proposed inverse technique is not deteriorated when sensor outputs have a normal distribution noise variance of few percents. Lastly, a good engineering practice would be to stop the reconstruction process according to an extended discrepancy principle including modeling and measurement errors. As shown in the article, the quality of the reconstructed field declines after reaching the threshold of the modeling error.

Experimental characterization of the constitutive materials composing an old masonry vaulted tunnel of the Paris subway system

ABSTRACT A significant proportion of the Paris metro tunnels comprise a masonry vault built out of stone blocks and mortar joints, and sidewalls and slabs made of unreinforced concrete. In order to provide the necessary data for future structural evaluation, an extensive laboratory testing programme has been conducted to characterize the materials of the tunnel separately, i.e., mortar, stone, and concrete. The tests, carried out on specimens taken from cores extracted from a 1930s tunnel, enabled to determine the mechanical properties, including direct tensile, shear strength, and mode I fracture energy, as well as the properties of the stone-mortar interface. Results show that the masonry mortar joints could reach 10 cm in width, and that blocks of stone varied in composition and porosity, thus producing a wide range of mechanical properties. The concrete was composed of large-sized aggregates and showed low stiffness and strength. Based on these experimental results, ratios between mechanical characteristics are hereby proposed. Perspectives on the use of this experimental data in a finite element model are then discussed.

Adjoint-based numerical method using standard engineering software for the optimal placement of chlorine sensors in drinking water networks

To obtain representative water quality simulations, unknown model parameters have to be updated by combining information from the water quality model and the sensor outputs. An adjoint-based numerical method has been developed to determine the optimal placement of chlorine sensors in drinking water networks at a low computational cost. From a practical engineering perspective, the proposed optimal placement corresponds to the set of sensors that minimizes the area in which the unknown model parameters cannot be identified. The numerical strategy is implemented in the hydraulic software EPANET. Using the adjoint framework, we develop and apply an adaptive strategy in a French drinking water network that provides the optimal placement from 1 sensor to 6 sensors. We show that the highest reduction of the non-identifiable area is obtained at the first stages of the adaptive strategy. After 4 sensors, a plateau is reached. Reliable water quality simulations can be reached by updating the reaction coefficient.The adjoint state allows to localize the non-coverage area for a given set of sensors.An adaptive strategy is applied to optimally place 1 to 6 sensors in a French network.The adaptive strategy is implemented in EPANET software.First stages of the adaptive strategy give the highest decrease of the non-coverage area.

Extension of Petersen matrix to the modelling of chemical equilibrium involved in concrete carbonation

Concrete is a porous material in which several chemical reactions may develop. One way to handle such a complex set of reactions is to use a modified form of Petersen matrix notation which is described in the paper. This formulation of Petersen matrix is able to handle the case where some of the reactions involved in the set of reactions have no analytical expression, but are described by chemical equilibrium. In order to handle this new situation, the reaction rate is tuned during the simulations in such a way that the chemical equilibrium remains verified. This tuning is performed thanks to a numerical proportional integral (PI) controller technique. This extension of the Petersen matrix is applied to the case of concrete carbonation modelling. The PI coefficients are given for each equilibrium controlled kinetics. The simulation results obtained thanks to a finite-difference solver are compared to experimental results taken from the literature.