Universität Stuttgart
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Item Open Access Learning groundwater contaminant diffusion‐sorption processes with a finite volume neural network(2022) Praditia, Timothy; Karlbauer, Matthias; Otte, Sebastian; Oladyshkin, Sergey; Butz, Martin V.; Nowak, WolfgangImproved understanding of complex hydrosystem processes is key to advance water resources research. Nevertheless, the conventional way of modeling these processes suffers from a high conceptual uncertainty, due to almost ubiquitous simplifying assumptions used in model parameterizations/closures. Machine learning (ML) models are considered as a potential alternative, but their generalization abilities remain limited. For example, they normally fail to predict accurately across different boundary conditions. Moreover, as a black box, they do not add to our process understanding or to discover improved parameterizations/closures. To tackle this issue, we propose the hybrid modeling framework FINN (finite volume neural network). It merges existing numerical methods for partial differential equations (PDEs) with the learning abilities of artificial neural networks (ANNs). FINN is applied on discrete control volumes and learns components of the investigated system equations, such as numerical stencils, model parameters, and arbitrary closure/constitutive relations. Consequently, FINN yields highly interpretable results. We demonstrate FINN's potential on a diffusion‐sorption problem in clay. Results on numerically generated data show that FINN outperforms other ML models when tested under modified boundary conditions, and that it can successfully differentiate between the usual, known sorption isotherms. Moreover, we also equip FINN with uncertainty quantification methods to lay open the total uncertainty of scientific learning, and then apply it to a laboratory experiment. The results show that FINN performs better than calibrated PDE‐based models as it is able to flexibly learn and model sorption isotherms without being restricted to choose among available parametric models.Item Open Access Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces(2020) Erdal, Daniel; Xiao, Sinan; Nowak, Wolfgang; Cirpka, Olaf A.Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70-90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.Item Open Access An adaptive hybrid vertical equilibrium/full‐dimensional model for compositional multiphase flow(2022) Becker, Beatrix; Guo, Bo; Buntic, Ivan; Flemisch, Bernd; Helmig, RainerEfficient compositional models are required to simulate underground gas storage in porous formations where, for example, gas quality (such as purity) and loss of gas due to dissolution are of interest. We first extend the concept of vertical equilibrium (VE) to compositional flow, and derive a compositional VE model by vertical integration. Second, we present a hybrid model that couples the efficient compositional VE model to a compositional full‐dimensional model. Subdomains, where the compositional VE model is valid, are identified during simulation based on a VE criterion that compares the vertical profiles of relative permeability at equilibrium to the ones simulated by the full‐dimensional model. We demonstrate the applicability of the hybrid model by simulating hydrogen storage in a radially symmetric, heterogeneous porous aquifer. The hybrid model shows excellent adaptivity over space and time for different permeability values in the heterogeneous region, and compares well to the full‐dimensional model while being computationally efficient, resulting in a runtime of roughly one‐third of the full‐dimensional model. Based on the results, we assume that for larger simulation scales, the efficiency of this new model will increase even more.Item Open Access Obstacles, interfacial forms, and turbulence : a numerical analysis of soil-water evaporation across different interfaces(2020) Coltman, Edward; Lipp, Melanie; Vescovini, Andrea; Helmig, RainerExchange processes between a turbulent free flow and a porous media flow are sensitive to the flow dynamics in both flow regimes, as well as to the interface that separates them. Resolving these complex exchange processes across irregular interfaces is key in understanding many natural and engineered systems. With soil-water evaporation as the natural application of interest, the coupled behavior and exchange between flow regimes are investigated numerically, considering a turbulent free flow as well as interfacial forms and obstacles. Interfacial forms and obstacles will alter the flow conditions at the interface, creating flow structures that either enhance or reduce exchange rates based on their velocity conditions and their mixing with the main flow. To evaluate how these interfacial forms change the exchange rates, interfacial conditions are isolated and investigated numerically. First, different flow speeds are compared for a flat surface. Second, a porous obstacle of varied height is introduced at the interface, and the effects the flow structures that develop have on the interface are analyzed. The flow parameters of this obstacle are then varied and the interfacial exchange rates investigated. Next, to evaluate the interaction of flow structures between obstacles, a second obstacle is introduced, separated by a varied distance. Finally, the shape of these obstacles is modified to create different wave forms. Each of these interfacial forms and obstacles is shown to create different flow structures adjacent to the surface which alter the mass, momentum, and energy conditions at the interface. These changes will enhance the exchange rate in locations where higher velocity gradients and more mixing with the main flow develop, but will reduce the exchange rate in locations where low velocity gradients and limited mixing with the main flow occur.Item Open Access A dual-continuum approach for precipitated salt in porous media : accounting for coupled transport processes(2026) Grether, Simon; Kostelecky, Anna Mareike; Kiemle, Stefanie; Schneider, Martin; Helmig, RainerSalt precipitation in porous media can negatively impact environmental systems. It enhances the evaporation process and thereby leads to a faster drying of soils. To address this, we introduce a dual-continuum modeling framework that enables the simulation of fluid flow in both the original, main porous structure, referred to as porous matrix, and the newly formed salt structure. We present two modeling strategies: (1) a coupled-flow model that explicitly resolves mass and energy transport in both the matrix and salt continua, incorporating advective, diffusive, and filling-based exchange terms; and (2) a pseudo-flow model that assumes full saturation of the salt continuum and implicitly captures flow based on evaporative demand, improving computational efficiency. Both approaches reproduce expected saturation profiles, temperature distributions, and evaporation behavior. The resulting evaporation rates are increased, leading to a faster drying out of the porous medium compared to a single-continuum model. The coupled-flow model shows that the precipitated salt remains liquid-saturated for a longer period than the surrounding matrix, thereby sustaining upward water transport; however, its results are sensitive to the parameterization. By assuming full saturation of the precipitated salt, the pseudo-flow model yields the higher evaporation rates while also improving numerical stability. This work presents a first step toward modeling the coupled transport processes resulting from salt precipitation in porous media.Item Open Access The role of retardation, attachment and detachment processes during microbial coal-bed methane production after organic amendment(2020) Emmert, Simon; Davis, Katherine; Gerlach, Robin; Class, HolgerMicrobially enhanced coal-bed methane could allow for a more sustainable method of harvesting methane from un-mineable coaldbeds. The model presented here is based on a previously validated batch model; however, this model system is based on upflow reactor columns compared to previous experiments and now includes flow, transport and reactions of amendment as well as intermediate products. The model implements filtration and retardation effects, biofilm decay, and attachment and detachment processes of microbial cells due to shear stress. The model provides additional insights into processes that cannot be easily observed in experiments. This study improves the understanding of complex and strongly interacting processes involved in microbially enhanced coal-bed methane production and provides a powerful tool able to model the entire process of enhancing methane production and transport during microbial stimulation.Item Open Access Thermochemical heat storage in a lab-scale indirectly operated CaO/Ca(OH)2 reactor - numerical modeling and model validation through inverse parameter estimation(2021) Seitz, Gabriele; Mohammadi, Farid; Class, HolgerCalcium oxide/Calcium hydroxide can be utilized as a reaction system for thermochemical heat storage. It features a high storage capacity, is cheap, and does not involve major environmental concerns. Operationally, different fixed-bed reactor concepts can be distinguished; direct reactor are characterized by gas flow through the reactive bulk material, while in indirect reactors, the heat-carrying gas flow is separated from the bulk material. This study puts a focus on the indirectly operated fixed-bed reactor setup. The fluxes of the reaction fluid and the heat-carrying flow are decoupled in order to overcome limitations due to heat conduction in the reactive bulk material. The fixed bed represents a porous medium where Darcy-type flow conditions can be assumed. Here, a numerical model for such a reactor concept is presented, which has been implemented in the software DuMux. An attempt to calibrate and validate it with experimental results from the literature is discussed in detail. This allows for the identification of a deficient insulation of the experimental setup. Accordingly, heat-loss mechanisms are included in the model. However, it can be shown that heat losses alone are not sufficient to explain the experimental results. It is evident that another effect plays a role here. Using Bayesian inference, this effect is identified as the reaction rate decreasing with progressing conversion of reactive material. The calibrated model reveals that more heat is lost over the reactor surface than transported in the heat transfer channel, which causes a considerable speed-up of the discharge reaction. An observed deceleration of the reaction rate at progressed conversion is attributed to the presence of agglomerates of the bulk material in the fixed bed. This retardation is represented phenomenologically by modifying the reaction kinetics. After the calibration, the model is validated with a second set of experimental results. To speed up the calculations for the calibration, the numerical model is replaced by a surrogate model based on Polynomial Chaos Expansion and Principal Component Analysis.Item Open Access Hydrological modelling in data sparse environment : inverse modelling of a historical flood event(2020) Bárdossy, András; Anwar, Faizan; Seidel, JochenWe dealt with a rather frequent and difficult situation while modelling extreme floods, namely, model output uncertainty in data sparse regions. A historical extreme flood event was chosen to illustrate the challenges involved. Our aim was to understand what the causes might have been and specifically to show how input and model parameter uncertainties affect the output. For this purpose, a conceptual model was calibrated and validated with recent data rich time period. Resulting model parameters were used to model the historical event which subsequently resulted in a rather poor hydrograph. Due to the bad model performance, a spatial simulation technique was used to invert the model for precipitation. Constraints, such as taking the precipitation values at historical observation locations in to account, with correct spatial structures and following the observed regional distributions were used to generate realistic precipitation fields. Results showed that the inverted precipitation improved the performance significantly even when using many different model parameters. We conclude that while modelling in data sparse conditions both model input and parameter uncertainties have to be dealt with simultaneously to obtain meaningful results.Item Open Access A three-dimensional homogenization approach for effective heat transport in thin porous media(2022) Scholz, Lena; Bringedal, CarinaHeat transport through a porous medium depends on the local pore geometry and on the heat conductivities of the solid and the saturating fluid. Through upscaling using formal homogenization, the local pore geometry can be accounted for to derive effective heat conductivities to be used at the Darcy scale. We here consider thin porous media, where not only the local pore geometry plays a role for determining the effective heat conductivity, but also the boundary conditions applied at the top and the bottom of the porous medium. Assuming scale separation and using two-scale asymptotic expansions, we derive cell problems determining the effective heat conductivity, which incorporates also the effect of the boundary conditions. Through solving the cell problems, we show how the local grain shape, and in particular its surface area at the top and bottom boundary, affects the effective heat conductivity through the thin porous medium.Item Open Access Fuzzy map comparisons enable objective hydro‐morphodynamic model validation(2021) Negreiros, Beatriz; Schwindt, Sebastian; Haun, Stefan; Wieprecht, SilkeNumerical modeling represents a state‐of‐the‐art technique to simulate hydro‐morphodynamic processes in river ecosystems. Numerical models are often validated based on observed topographic change in the form of pixel information on net erosion or deposition over a simulation period. When model validation is performed by a pixel‐by‐pixel comparison of exactly superimposed simulated and observed pixels, zero or negative correlation coefficients are often calculated, suggesting poor model performance. Thus, a pixel‐by‐pixel approach penalizes quantitative simulation errors, even if a model conceptually works well. To distinguish between reasonably well‐performing and non‐representative models, this study introduces and tests fuzzy map comparison methods. First, we use a fuzzy numerical map comparison to compensate for spatial offset errors in correlation analyses. Second, we add a level of fuzziness with a fuzzy kappa map comparison to additionally address quantitative inaccuracy in modeled topographic change by categorizing data. Sample datasets from a physical lab model and datasets from a 6.9 km long gravel-cobble bed river reach enable the verification of the relevance of fuzzy map comparison methods. The results indicate that a fuzzy numerical map comparison is a viable technique to compensate for model errors stemming from spatial offset. In addition, fuzzy kappa map comparisons are suitable for objectively expressing subjectively perceived correlation between two maps, provided that a small number of categories is used. The methods tested and the resulting spatially explicit comparison maps represent a significant opportunity to improve the evaluation and potential calibration of numerical models of river ecosystems in the future.