Use of Global Sensitivity Analysis and Polynomial Chaos Expansion for Interpretation of Non-reactive Transport Experiments in Laboratory-Scale Porous Media

International audienceIn this work, we show how the use of global sensitivity analysis (GSA) in conjunction with the polynomial chaos expansion (PCE) methodology can provide relevant information for the interpretation of transport experiments in laboratory-scale heterogeneous porous media. We perform GSA by calculating the Sobol indices, which provide a variance-based importance measure of the effects of uncertain parameters on the output of a chosen interpretive transport model. The choice of PCE has the following two benefits: (1) it provides the global sensitivity indices in a straightforward manner, and (2) PCE can serve as a surrogate model for the calibration of parameters. The coefficients of the PCE are computed by probabilistic collocation. The methodology is applied to two nonreactive transport experiments available in the literature, while considering both transient and pseudo steady state transport regimes. This method allows a rigorous investigation of the relative effects and importance of different uncertain quantities, which include boundary conditions as well as porous medium hydraulic and dispersive parameters. The parameters that are most relevant to depicting the system's behavior can then be evaluated. In addition, one can assess the space-time distribution of measurement points, which is the most influential factor for the identifiability of parameters. Our work indicates that these methods can be valuable tools in the proper design of model-based transport experiments

Finite volume method in curvilinear coordinates for hyperbolic conservation laws

International audienceThis paper deals with the design of finite volume approximation of hyperbolic conservation laws in curvilinear coordinates. Such coordinates are encountered naturally in many problems as for instance in the analysis of a large number of models coming from magnetic confinement fusion in tokamaks. In this paper we derive a new finite volume method for hyperbolic conservation laws in curvilinear coordinates. The method is first described in a general setting and then is illustrated in 2D polar coordinates. Numerical experiments show its advantages with respect to the use of Cartesian coordinates

Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

We present an inverse modeling procedure for the estimation of model parameters of sedi- mentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophys- ical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likeli- hood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quanti- fied through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approxi- mations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored

Impact of space-time mesh adaptation on solute transport modeling in porous media

open4siWe implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of non-reactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape and orientation of the mesh elements. Adaptation of the time step is performed through an ad-hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a non-uniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization.openEsfandiar, B; Porta, G; Perotto, S; Guadagnini, AESFANDIAR JAHROMI, Bahman; Porta, GIOVANNI MICHELE; Perotto, Simona; Guadagnini, Albert

Association between infection with H. pylori and atopy in young Ethiopian children: a longitudinal study

Background: Epidemiological evidence from developed countries indicates that Helicobacter pylori infection correlates with a reduced risk of atopy and allergic disorders, however limited data are available from low-income countries. Objective: We examined associations between H. pylori infection in early childhood and atopy and reported allergic disorders at the age of 6.5 years in an Ethiopian birth cohort. Methods: A total of 856 children (85.1% of the 1006 original singletons in a population-based birth cohort) were followed up at age six and half years. An interviewer-led questionnaire administered to mothers provided information on demographic and lifestyle variables. Questions on allergic disease symptoms were based on the International Study of Asthma and Allergies in Children (ISAAC) core allergy and environmental questionnaire. Serum samples were analysed for total IgE levels and anti-H. pylori cytotoxin associated gene A (CagA) IgG antibody using commercially available ELISA kits. Stool samples were analysed for H. pylori antigen using a rapid immunochromatographic test. The independent effects of H. pylori infection (measured at age 3, 5 and 6.5 years) on prevalence and incidence of atopy and reported allergic disorders (measured at age 6.5 years) were determined using multiple logistic regression. Results: In cross-sectional analysis, current H. pylori infection at age 6.5 years was inversely, though not significantly, related to prevalence of atopy and ‘any allergic condition’ at age 6.5 years. However detection of H. pylori infection at any point up to age 6.5 years was associated with a significantly reduced odds of both atopy and ‘any allergic condition’ (adjusted OR AOR, 95% CI, 0.54; 0.32 to 0.92, p=0.02, and 0.31; 0.10 to 0.94, p=0.04, respectively). In longitudinal analyses, H. pylori infection at age 3 was inversely associated with incidence of atopy (AOR, 95% CI, 0.49; 0.27 to 0.89, p=0.02). Furthermore, among H. pylori infected children, those with a CagA+ strain had a more pronounced reduction in odds of atopy (AOR=0.35 vs. 0.63 for CagA+ vs. CagA-) and this reduction reached borderline significance. Conclusion: These data are consistent with the hypothesis that early exposure to H. pylori is inversely associated with atopy and allergic conditions. A possible modest protective association against atopy was observed in those infected with a more virulent CagA+ strain of H. pylori. This article is protected by copyright. All rights reserved

Sensitivity analysis and polynomial chaos expansion for parameter estimation : application to transfer in porous media

La gestion des transferts des contaminants en milieu poreux représentent une préoccupation croissante et revêtent un intérêt particulier pour le contrôle de la pollution dans les milieux souterrains et la gestion de la ressource en eau souterraine, ou plus généralement la protection de l’environnement. Les phénomènes d’écoulement et de transport de polluants sont décrits par des lois physiques traduites sous forme d'équations algébro-différentielles qui dépendent d'un grand nombre de paramètres d'entrée. Pour la plupart, ces paramètres sont mal connus et souvent ne sont pas directement mesurables et/ou leur mesure peut être entachée d’incertitude. Ces travaux de thèse concernent l’étude de l’analyse de sensibilité globale et l’estimation des paramètres pour des problèmes d’écoulement et de transport en milieux poreux. Pour mener à bien ces travaux, la décomposition en polynômes de chaos est utilisée pour quantifier l'influence des paramètres sur la sortie des modèles numériques utilisés. Cet outil permet non seulement de calculer les indices de sensibilité de Sobol mais représente également un modèle de substitution (ou métamodèle) beaucoup plus rapide à exécuter. Cette dernière caractéristique est alors exploitée pour l'inversion des modèles à partir des données observées. Pour le problème inverse, nous privilégions l'approche Bayésienne qui offre un cadre rigoureux pour l'estimation des paramètres. Dans un second temps, nous avons développé une stratégie efficace permettant de construire des polynômes de chaos creux, où seuls les coefficients dont la contribution sur la variance du modèle est significative, sont retenus. Cette stratégie a donné des résultats très encourageants pour deux problèmes de transport réactif. La dernière partie de ce travail est consacrée au problème inverse lorsque les entrées du modèle sont des champs stochastiques gaussiens spatialement distribués. La particularité d'un tel problème est qu'il est mal posé car un champ stochastique est défini par une infinité de coefficients. La décomposition de Karhunen-Loève permet de réduire la dimension du problème et également de le régulariser. Toutefois, les résultats de l'inversion par cette méthode fournit des résultats sensibles au choix à priori de la fonction de covariance du champ. Un algorithme de réduction de la dimension basé sur un critère de sélection (critère de Schwartz) est proposé afin de rendre le problème moins sensible à ce choix.The management of transfer of contaminants in porous media is a growing concern and is of particular interest for the control of pollution in underground environments and management of groundwater resources, or more generally the protection of the environment. The flow and transport of pollutants are modeled by physical and phenomenological laws that take the form of differential-algebraic equations. These models may depend on a large number of input parameters. Most of these parameters are well known and are often not directly observable.This work is concerned with the impact of parameter uncertainty onto model predictions. To this end, the uncertainty and sensitivity analysis is an important step in the numerical simulation, as well as inverse modeling. The first study consists in estimating the model predictive uncertainty given the parameters uncertainty and identifying the most relevant ones. The second study is concerned with the reduction of parameters uncertainty from available observations.This work concerns the study of global sensitivity analysis and parameter estimation for problems of flow and transport in porous media. To carry out this work, the polynomials chaos expansion is used to quantify the influence of the parameters on the predictions of the numerical model. This tool not only calculate Sobol' sensitivity indices but also provides a surrogate model (or metamodel) that is faster to run. This feature is then exploited for models inversion when observations are available. For the inverse problem, we focus on Bayesian approach that offers a rigorous framework for parameter estimation.In a second step, we developed an effective strategy for constructing a sparse polynomials chaos expansion, where only coefficients whose contribution to the variance of the model is significant, are retained. This strategy has produced very encouraging results for two reactive transport problems.The last part of this work is devoted to the inverse problem when the inputs of the models are spatially distributed. Such an input is then treated as stochastic fields. The peculiarity of such a problem is that it is ill-posed because a stochastic field is defined by an infinite number of coefficients. The Karhunen-Loeve reduces the dimension of the problem and also allows regularizing it. However, the inversion with this method provides results that are sensitive to the presumed covariance function. An algorithm based on the selection criterion (Schwartz criterion) is proposed to make the problem less sensitive to this choice

Study of gene expression of six genes after pre partum vitamin D3 treatment in dairy cows

My thesis main objective was to investigate the possible beneficial effects of vitamin D3 supplementation on the immune and reproductive system in pregnant Holstein-Friesian breed through analysing the expression of six genes using the real-time PCR method.MSc/MAAnimal Husbandry Engineerin

Analyse de sensibilité globale et polynômes de chaos pour l'estimation des paramètres : application aux transferts en milieu poreux

The management of transfer of contaminants in porous media is a growing concern and is of particular interest for the control of pollution in underground environments and management of groundwater resources, or more generally the protection of the environment. The flow and transport of pollutants are modeled by physical and phenomenological laws that take the form of differential-algebraic equations. These models may depend on a large number of input parameters. Most of these parameters are well known and are often not directly observable.This work is concerned with the impact of parameter uncertainty onto model predictions. To this end, the uncertainty and sensitivity analysis is an important step in the numerical simulation, as well as inverse modeling. The first study consists in estimating the model predictive uncertainty given the parameters uncertainty and identifying the most relevant ones. The second study is concerned with the reduction of parameters uncertainty from available observations.This work concerns the study of global sensitivity analysis and parameter estimation for problems of flow and transport in porous media. To carry out this work, the polynomials chaos expansion is used to quantify the influence of the parameters on the predictions of the numerical model. This tool not only calculate Sobol' sensitivity indices but also provides a surrogate model (or metamodel) that is faster to run. This feature is then exploited for models inversion when observations are available. For the inverse problem, we focus on Bayesian approach that offers a rigorous framework for parameter estimation.In a second step, we developed an effective strategy for constructing a sparse polynomials chaos expansion, where only coefficients whose contribution to the variance of the model is significant, are retained. This strategy has produced very encouraging results for two reactive transport problems.The last part of this work is devoted to the inverse problem when the inputs of the models are spatially distributed. Such an input is then treated as stochastic fields. The peculiarity of such a problem is that it is ill-posed because a stochastic field is defined by an infinite number of coefficients. The Karhunen-Loeve reduces the dimension of the problem and also allows regularizing it. However, the inversion with this method provides results that are sensitive to the presumed covariance function. An algorithm based on the selection criterion (Schwartz criterion) is proposed to make the problem less sensitive to this choice.La gestion des transferts des contaminants en milieu poreux représentent une préoccupation croissante et revêtent un intérêt particulier pour le contrôle de la pollution dans les milieux souterrains et la gestion de la ressource en eau souterraine, ou plus généralement la protection de l’environnement. Les phénomènes d’écoulement et de transport de polluants sont décrits par des lois physiques traduites sous forme d'équations algébro-différentielles qui dépendent d'un grand nombre de paramètres d'entrée. Pour la plupart, ces paramètres sont mal connus et souvent ne sont pas directement mesurables et/ou leur mesure peut être entachée d’incertitude. Ces travaux de thèse concernent l’étude de l’analyse de sensibilité globale et l’estimation des paramètres pour des problèmes d’écoulement et de transport en milieux poreux. Pour mener à bien ces travaux, la décomposition en polynômes de chaos est utilisée pour quantifier l'influence des paramètres sur la sortie des modèles numériques utilisés. Cet outil permet non seulement de calculer les indices de sensibilité de Sobol mais représente également un modèle de substitution (ou métamodèle) beaucoup plus rapide à exécuter. Cette dernière caractéristique est alors exploitée pour l'inversion des modèles à partir des données observées. Pour le problème inverse, nous privilégions l'approche Bayésienne qui offre un cadre rigoureux pour l'estimation des paramètres. Dans un second temps, nous avons développé une stratégie efficace permettant de construire des polynômes de chaos creux, où seuls les coefficients dont la contribution sur la variance du modèle est significative, sont retenus. Cette stratégie a donné des résultats très encourageants pour deux problèmes de transport réactif. La dernière partie de ce travail est consacrée au problème inverse lorsque les entrées du modèle sont des champs stochastiques gaussiens spatialement distribués. La particularité d'un tel problème est qu'il est mal posé car un champ stochastique est défini par une infinité de coefficients. La décomposition de Karhunen-Loève permet de réduire la dimension du problème et également de le régulariser. Toutefois, les résultats de l'inversion par cette méthode fournit des résultats sensibles au choix à priori de la fonction de covariance du champ. Un algorithme de réduction de la dimension basé sur un critère de sélection (critère de Schwartz) est proposé afin de rendre le problème moins sensible à ce choix