Alain Vande Wouwer

Model selection, identification and validation in anaerobic digestion: A review

Anaerobic digestion enables waste (water) treatment and energy production in the form of biogas. The successful implementation of this process has lead to an increasing interest worldwide. However, anaerobic digestion is a complex biological process, where hundreds of microbial populations are involved, and whose start-up and operation are delicate issues. In order to better understand the process dynamics and to optimize the operating conditions, the availability of dynamic models is of paramount importance. Such models have to be inferred from prior knowledge and experimental data collected from real plants. Modeling and parameter identification are vast subjects, offering a realm of approaches and methods, which can be difficult to fully understand by scientists and engineers dedicated to the plant operation and improvements. This review article discusses existing modeling frameworks and methodologies for parameter estimation and model validation in the field of anaerobic digestion processes. The point of view is pragmatic, intentionally focusing on simple but efficient methods.

A detailed metabolic flux analysis of an underdetermined network of CHO cells

In this article the metabolic flux analysis of growing CHO-320 cells is performed for a detailed metabolic network which involves 100 reactions and embraces all the significant pathways describing the metabolism of CHO cells. The purpose is to investigate the efficiency of the flux analysis when it is based on a relatively small set of extracellular measurements that can be easily achieved in most laboratories. In this case the flux analysis problem leads to a generally underdetermined mass balance system, as data are not sufficient to uniquely define the metabolic fluxes. Our main contribution is to show that, provided the system of mass balance equations is well-posed, although it is underdetermined, very narrow intervals may be found for most fluxes. The importance of checking the well-posedness of the problem is emphasized and the influence of the number of available measurements on the accuracy of the metabolic flux intervals is systematically investigated. In all cases the computed flux intervals are bounded and a single well defined value is obtained for the formation rates of the cellular macromolecules (proteins, DNA, RNA, lipids) that are not measured. The potential gain of a simple theoretical assumption regarding the metabolism of Threonine is also discussed and compared with an optimal solution calculated by maximizing the biomass formation rate. Alternative network structures obtained by inverting the direction of reversible reactions are also considered. Finally, the results of the metabolic flux analysis are exploited to estimate the total energy production resulting from the metabolism of growing CHO-320 cells.

Brief paper: Fast computation of minimal elementary decompositions of metabolic flux vectors

The concept of elementary flux vector is valuable in a number of applications of metabolic engineering. For instance, in metabolic flux analysis, each admissible flux vector can be expressed as a non-negative linear combination of a small number of elementary flux vectors. However a critical issue concerns the total number of elementary flux vectors which may be huge because it combinatorially increases with the size of the metabolic network. In this paper we present a fast algorithm that randomly computes a decomposition of admissible flux vectors in a minimal number of elementary flux vectors without explicitly enumerating all of them.

An optimizing start-up strategy for a bio-methanator

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang–bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.

On the Optimization of Biogas Production in Anaerobic Digestion Systems

Abstract This paper presents a strategy for the optimization of biogas outflow rate in an anaerobic digestion process described by a two-population model. The methodology relies on the solution of two optimization problems: steady state optimization for determining the optimal operating point and transient optimization. The latter is solved using the maximum principle of Pontryagin. The proposed control law, which drives the process from an initial state to the optimal steady state while maximizing the biogas outflow rate, consists of switching the manipulated variable (dilution rate) from the minimum to the maximum value and then to the optimal value at well defined instants. This control law substantially increases the stability region of the optimal equilibrium point, enlarging it in some cases to almost the entire state space. Aside its efficiency, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are respectively characterized by Monod and Haldane kinetics.

A dynamical interpretation of strong observability and detectability concepts for nonlinear systems with unknown inputs: application to biochemical processes

Determination of the observability/detectability properties of a nonlinear system is fundamental to assess the possibility of constructing observers and the properties that can be assigned to them, as e.g., the assignability of the convergence rate. For linear systems this task can be solved by well-known techniques, for the case without perturbations as much as for the perturbed case. However, for nonlinear systems this study is usually a very hard task, in particular, when unknown inputs and/or perturbations are present. In this paper a general method to study these properties will be described, and its capabilities and feasibility will be assessed by means of a few case studies related to the culture of phytoplankton in the chemostat.

Stoichiometric identification with maximum likelihood principal component analysis

This study presents an effective procedure for the determination of a biologically inspired, black-box model of cultures of microorganisms (including yeasts, bacteria, plant and animal cells) in bioreactors. This procedure is based on sets of experimental data measuring the time-evolution of a few extracellular species concentrations, and makes use of maximum likelihood principal component analysis to determine, independently of the kinetics, an appropriate number of macroscopic reactions and their stoichiometry. In addition, this paper provides a discussion of the geometric interpretation of a stoichiometric matrix and the potential equivalent reaction schemes. The procedure is carefully evaluated within the stoichiometric identification framework of the growth of the yeast Kluyveromyces marxianus on cheese whey. Using Monte Carlo studies, it is also compared with two other previously published approaches.

Accelerating animal cell growth in perfusion mode by multivariable control: simulation studies

This study considers the problem of manipulating in an optimal way the perfusion and bleed flow rates of a continuous culture of hybridoma cells, so as to achieve a fast transient start-up and reject potential disturbances. The proposed solution makes use of an analysis of the properties of the steady state solutions of the nonlinear dynamic model of the cell culture, and in particular the relationship between the two main limiting substrates, glucose and glutamine. The solution is implemented using extended prediction self-adaptive control. Simulation results demonstrate the approach potentiality.

Design and test of a low-cost RGB sensor for online measurement of microalgae concentration within a photo-bioreactor.

In this study, a low-cost RGB sensor is developed to measure online the microalgae concentration within a photo-bioreactor. Two commercially available devices, i.e., a spectrophotometer for offline measurements and an immersed probe for online measurements, are used for calibration and comparison purposes. Furthermore, the potential of such a sensor for estimating other variables is illustrated with the design of an extended Luenberger observer.

Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection

Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.