An Efficient Implementation of the Method of Lines for Multicomponent Reactive Transport Equations

Fahs, Marwan; Younès, Anis; Ackerer, Philippe

doi:10.1007/s11270-010-0477-y

Cited by 12 publications

(11 citation statements)

References 46 publications

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“…This experiment is representative of several laboratory SP experiments (Linde et al, 2007; Allegre et al has an exponential behavior driven by the saturated conductivity (Miller et al, 1998;Younes et al, 2009;Fahs et al, 2009Fahs et al, , 2011.…”

Section: Conceptual Model and Numerical Solutionmentioning

confidence: 91%

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Younès¹,

Zaouali²,

Lehmann³

et al. 2018

Preprint

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Abstract. Fluid flow in a charged porous medium generates electric potentials called Streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, Global Sensitivity Analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse Polynomial Chaos Expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap Information Criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method and the First-Order Approximation (FOA) approach based on the Levenberg Marquardt algorithm. GSA results show that at short times, the saturated hydraulic conductivity (KS) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas, at long times, the residual water content (σr), the Mualem-van Genuchten parameter (n) and the Archies’s saturation exponent (na) become influential with strong interactions between them. The Mualem-van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that, although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (KS, σr, and n) and geophysical (na and Csat) parameters can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

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Section: Conceptual Model and Numerical Solutionmentioning

confidence: 91%

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Younès¹,

Zaouali²,

Lehmann³

et al. 2018

Preprint

Self Cite

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show abstract

“…The aim of GSA is to assess the effect of the variation of parameters on the model output (Mara and Tarantola, 2008). Such knowledge is important for determining the most influential parameters as well as their regions and periods of influence (Fajraoui et al, 2011). The sensitivity of a model to its parameters can be assessed using variance-based sensitivity indices.…”

Section: Gsa Methodsmentioning

confidence: 99%

“…This is a useful tool for characterizing the influential parameters that contribute the most to the variability of model outputs (Saltelli et al,1999;Sudret, 2008) and for understanding the behavior of the modeled system. GSA has been applied in several areas, for risk assessment for groundwater pollution (e.g., Volkova et al, 2008), nonreactive (Fajraoui et al, 2011) and reactive transport experiments (Fajraoui et al, 2012;Younes et al, 2016), for unsaturated flow experiments , natural convection in porous media (Fajraoui et al, 2017) and seawater intrusion (Rajabi et al, 2015;Riva et al, 2015). To the best of our knowledge, GSA has never been used for SP signals in unsaturated porous media.…”

mentioning

confidence: 99%

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Younès

Zaouali

Lehmann

et al. 2018

Hydrol. Earth Syst. Sci.

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Abstract. Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg–Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly nonlinear hydrogeophysical problem investigated. GSA results show that in short time periods, the saturated hydraulic conductivity (Ks) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas in long time periods, the residual water content (θs), the Mualem–van Genuchten parameter (n) and the Archie saturation exponent (na) become influential, with strong interactions between them. The Mualem–van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (Ks,θs,α,n) and geophysical parameters (na,Csat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

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“…Problem setting. We consider the field observations of Valocchi et al [44] that was used as a simulation benchmark by several authors ( [48,49,6,7]). The problem is a field experiment involving nonlinear ion exchange reactions in Palo Alto Baylands, California, where a multi-ion solution was injected into a well.…”

Section: Posterior Uncertainty Analysis Of the Cumulative Outflowmentioning

confidence: 99%

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

Mara¹,

Fahs²,

Shao³

et al. 2019

SIAM J. Sci. Comput.

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Random variables characterized by a joint probability distribution function (jpdf) defined in a Bayesian framework are generally sampled with Markov chain Monte Carlo (MCMC). The latter can be computationally demanding when the number of variables is high. As an alternative, the maximal conditional probability distribution (MCPD) sampler was recently introduced by some of the authors of the present article to readily and efficiently draw values randomly sampled from the desired jpdf. The MCPD approach provides the probability distribution of a given variable under the condition that the other variables maximized the conditional jpdf. However, contrarily to MCMC, MCPD does not provide enough draws to allow posterior uncertainty and sensitivity analyses of the computer model responses. In the present work, we show how to draw random samples from the MCPD draws under the requirement that the target jpdf possesses a particular dependence structure. Several numerical tests are carried out to prove the efficiency of the new sampling method. The new approach is used to perform the predictive uncertainty and sensitivity analyses of numerical models posterior to their statistical calibration from experimental data.

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An Efficient Implementation of the Method of Lines for Multicomponent Reactive Transport Equations

Cited by 12 publications

References 46 publications

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Random Sampling from Joint Probability Distributions Defined in a Bayesian Framework

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