Browsing by Author "Class, Holger"

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Open Access
Berechnung von Temperaturfahnen im Grundwasser mit analytischen und numerischen Modellen
(2022) Ohmer, Marc; Klester, Artur; Kissinger, Alexander; Mirbach, Stefan; Class, Holger; Schneider, Martin; Lindenlaub, Martin; Bauer, Michael; Liesch, Tanja; Menberg, Kathrin; Blum, Philipp
Mit zunehmender Anzahl an Grundwasserwärmepumpenanlagen steigt auch das Potenzial an Nutzungsüberlagerungen. Im Rahmen des wasserrechtlichen Genehmigungsverfahrens ist es daher erforderlich, u. a. die von einer Anlage ausgehenden Temperaturfahnen im Grundwasser zu berechnen. In Baden-Württemberg wurde als Erweiterung des für Anlagen ≤ 45.000 kWh/a gültigen Leitfadens des Umweltministeriums Baden-Württemberg das Thermische Online-Modell (TOM) entwickelt. Hierbei handelt es sich um ein vereinfachtes, browserbasiertes, numerisches Grundwassermodell. Ziel dieser Studie ist, die mit TOM berechneten Ausdehnungen von Temperaturfahnen durch mit analytisch und einem kalibrierten numerischen Modell berechnete Temperaturfahnen zu evaluieren. Der Vergleich mit den analytischen Berechnungsmethoden zeigt, dass diese die Ausbreitung der Temperaturfahnen in Relation zu den numerischen Modellen grundsätzlich überschätzen. Für kleine und mittlere Anlagen (< 10 l/s) wurden mit TOM vergleichbare Ergebnisse wie mit einem kalibrierten numerischen Modell berechnet. Für größere Anlagen (> 10 l/s) ist aufgrund der weiträumigeren Ausbreitung der Temperaturfelder die Simulation mit einem kalibrierten numerischen Planungsmodell zu empfehlen.
Open Access
Comparing different coupling and modeling strategies in hydromechanical models for slope stability assessment
(2024) Moradi, Shirin; Huisman, Johan Alexander; Vereecken, Harry; Class, Holger
The dynamic interaction between subsurface flow and soil mechanics is often simplified in the stability assessment of variably saturated landslide-prone hillslopes. The aim of this study is to analyze the impact of conventional simplifications in coupling and modeling strategies on stability assessment of such hillslopes in response to precipitation using the local factor of safety (LFS) concept. More specifically, it investigates (1) the impact of neglecting poroelasticity, (2) transitioning from full coupling between hydrological and mechanical models to sequential coupling, and (3) reducing the two-phase flow system to a one-phase flow system (Richards’ equation). Two rainfall scenarios, with the same total amount of rainfall but two different relatively high (4 mm h-1) and low (1 mm h-1) intensities are considered. The simulation results of the simplified approaches are compared to a comprehensive, fully coupled poroelastic hydromechanical model with a two-phase flow system. It was found that the most significant difference from the comprehensive model occurs in areas experiencing the most transient changes due to rainfall infiltration in all three simplified models. Among these simplifications, the transformation of the two-phase flow system to a one-phase flow system showed the most pronounced impact on the simulated local factor of safety (LFS), with a maximum increase of +21.5% observed at the end of the high-intensity rainfall event. Conversely, using a rigid soil without poroelasticity or employing a sequential coupling approach with no iteration between hydromechanical parameters has a relatively minor effect on the simulated LFS, resulting in maximum increases of +2.0% and +1.9%, respectively. In summary, all three simplified models yield LFS results that are reasonably consistent with the comprehensive poroelastic fully coupled model with two-phase flow, but simulations are more computationally efficient when utilizing a rigid porous media and one-phase flow based on Richards’ equation.
Open Access
Estimation of capillary‐associated NAPL‐water interfacial areas for unconsolidated porous media by kinetic interface sensitive (KIS) tracer method
(2023) Tatomir, Alexandru; Gao, Huhao; Abdullah, Hiwa; Pötzl, Christopher; Karadimitriou, Nikolaos; Steeb, Holger; Licha, Tobias; Class, Holger; Helmig, Rainer; Sauter, Martin
By employing kinetic interface sensitive (KIS) tracers, we investigate three different types of glass‐bead materials and three natural porous media systems to quantitatively characterize the influence of the porous‐medium grain‐, pore‐size and texture on the specific capillary‐associated interfacial area (FIFA) between an organic liquid and water. By interpreting the breakthrough curves (BTCs) of the reaction product of the KIS tracer hydrolysis, we obtain a relation for the specific IFA and wetting phase saturation. The immiscible displacement process coupled with the reactive tracer transport across the fluid-fluid interface is simulated with a Darcy‐scale numerical model. Linear relations between the specific capillary‐associated FIFA and the inverse mean grain diameter can be established for measurements with glass beads and natural soils. We find that the grain size has minimal effect on the capillary‐associated FIFA for unconsolidated porous media formed by glass beads. Conversely, for unconsolidated porous media formed by natural soils, the capillary‐associated FIFA linearly increases with the inverse mean grain diameter, and it is much larger than that from glass beads. This indicates that the surface roughness and the irregular shape of the grains can cause the capillary‐associated FIFA to increase. The results are also compared with the data collected from literature, measured with high resolution microtomography and partitioning tracer methods. Our study considerably expands the applicability range of the KIS tracers and enhances the confidence in the robustness of the method.
Open Access
Experimental and simulation study on validating a numerical model for CO2 density-driven dissolution in water
(2020) Class, Holger; Weishaupt, Kilian; Trötschler, Oliver
Carbon dioxide density-driven dissolution in a water-filled laboratory flume of the dimensions 60~cm length, 40~cm height, 1~cm thickness was visualized using a pH-sensitive color indicator. We focus on atmospheric pressure conditions, like in caves where CO2 concentrations are typically higher. Varying concentrations of carbon dioxide were applied as boundary conditions at the top of the experimental setup, leading to the onset of convective fingering at differing times. The data were used to validate a numerical model implemented in the numerical simulator Dumux. The model solves the Navier-Stokes equations for density-induced water flow with concentration-dependent fluid density and a transport equation including advective and diffusive processes for the carbon dioxide dissolved in water. The model was run in 2D, 3D, and pseudo-3D on two different grids. Without any calibration or fitting of parameters, the results of the comparison between experiment and simulation show satisfactory agreement with respect to the onset time of convective fingering as well as the number and the dynamics of the fingers. Grid refinement matters in particular in the uppermost part where fingers develop. The 2D simulations consistently overestimated the fingering dynamics. This successful validation of the model is the prequisite for employing it in situations with background flow and for a future study of karstification mechanisms related to CO2-induced fingering in caves.
Open Access
Experimental methods and imaging for enzymatically induced calcite precipitation in a microfluidic cell
(2021) Weinhardt, Felix; Class, Holger; Vahid Dastjerdi, Samaneh; Karadimitriou, Nikolaos; Lee, Dongwon; Steeb, Holger
Enzymatically induced calcite precipitation (EICP) in porous media can be used as an engineering option to achieve precipitation in the pore space, for example, aiming at a targeted sealing of existing flow paths. This is accomplished through a porosity and consequent permeability alteration. A major source of uncertainty in modeling EICP is in the quantitative description of permeability alteration due to precipitation. This report presents methods for investigating experimentally the time‐resolved effects of growing precipitates on porosity and permeability on the pore scale, in a poly‐di‐methyl‐siloxane microfluidic flow cell. These methods include the design and production of the microfluidic cells, the preparation and usage of the chemical solutions, the injection strategy, and the monitoring of pressure drops for given fluxes for the determination of permeability. EICP imaging methods are explained, including optical microscopy and X‐ray microcomputed tomography (XRCT), and the corresponding image processing and analysis. We present and discuss a new experimental procedure using a microfluidic cell, as well as the general perspectives for further experimental and numerical simulation studies on induced calcite precipitation. The results of this study show the enormous benefits and insights achieved by combining both light microscopy and XRCT with hydraulic measurements in microfluidic chips. This allows for a quantitative analysis of the evolution of precipitates with respect to their size and shape, while monitoring their influence on permeability. We consider this to be an improvement of the existing methods in the literature regarding the interpretation of recorded data (pressure, flux, and visualization) during pore morphology alteration.
Open Access
Experimental study on retardation of a heavy NAPL vapor in partially saturated porous media
(2017) Kleinknecht, Simon Matthias; Class, Holger; Braun, Jürgen
Non-aqueous-phase liquid (NAPL) contaminants introduced into the unsaturated zone spread as a liquid phase; however, they can also vaporize and migrate in a gaseous state. Vapor plumes migrate easily and thus pose a potential threat to underlying aquifers. Large-scale column experiments were performed to quantify partitioning processes responsible for the retardation of carbon disulfide (CS2) vapor in partially saturated porous media. The results were compared with a theoretical approach taking into account the partitioning into the aqueous phase as well as adsorption to the solid matrix and to the air–water interface. The experiments were conducted in large, vertical columns (i.d. of 0.109 m) of 2 m length packed with different porous media. A slug of CS2 vapor and the conservative tracer argon was injected at the bottom of the column followed by a nitrogen chase. Different seepage velocities were applied to characterize the transport and to evaluate their impact on retardation. Concentrations of CS2 and argon were measured at the top outlet of the column using two gas chromatographs. The temporal-moment analysis for step input was employed to evaluate concentration breakthrough curves and to quantify dispersion and retardation. The experiments conducted showed a pronounced retardation of CS2 in moist porous media which increased with water saturation. The comparison with an analytical solution helped to identify the relative contributions of partitioning processes to retardation. Thus, the experiments demonstrated that migrating CS2 vapor is retarded as a result of partitioning processes. Moreover, CS2 dissolved in the bulk water is amenable to biodegradation. The first evidence of CS2 decay by biodegradation was found in the experiments. The findings contribute to the understanding of vapor-plume transport in the unsaturated zone and provide valuable experimental data for the transfer to field-like conditions.
Open Access
The FluidFlower validation benchmark study for the storage of CO2
(2023) Flemisch, Bernd; Nordbotten, Jan M.; Fernø, Martin; Juanes, Ruben; Both, Jakub W.; Class, Holger; Delshad, Mojdeh; Doster, Florian; Ennis-King, Jonathan; Franc, Jacques; Geiger, Sebastian; Gläser, Dennis; Green, Christopher; Gunning, James; Hajibeygi, Hadi; Jackson, Samuel J.; Jammoul, Mohamad; Karra, Satish; Li, Jiawei; Matthäi, Stephan K.; Miller, Terry; Shao, Qi; Spurin, Catherine; Stauffer, Philip; Tchelepi, Hamdi; Tian, Xiaoming; Viswanathan, Hari; Voskov, Denis; Wang, Yuhang; Wapperom, Michiel; Wheeler, Mary F.; Wilkins, Andrew; Youssef, AbdAllah A.; Zhang, Ziliang
Successful deployment of geological carbon storage (GCS) requires an extensive use of reservoir simulators for screening, ranking and optimization of storage sites. However, the time scales of GCS are such that no sufficient long-term data is available yet to validate the simulators against. As a consequence, there is currently no solid basis for assessing the quality with which the dynamics of large-scale GCS operations can be forecasted. To meet this knowledge gap, we have conducted a major GCS validation benchmark study. To achieve reasonable time scales, a laboratory-size geological storage formation was constructed (the “FluidFlower”), forming the basis for both the experimental and computational work. A validation experiment consisting of repeated GCS operations was conducted in the FluidFlower, providing what we define as the true physical dynamics for this system. Nine different research groups from around the world provided forecasts, both individually and collaboratively, based on a detailed physical and petrophysical characterization of the FluidFlower sands. The major contribution of this paper is a report and discussion of the results of the validation benchmark study, complemented by a description of the benchmarking process and the participating computational models. The forecasts from the participating groups are compared to each other and to the experimental data by means of various indicative qualitative and quantitative measures. By this, we provide a detailed assessment of the capabilities of reservoir simulators and their users to capture both the injection and post-injection dynamics of the GCS operations.
Open Access
Heat transport from atmosphere through the subsurface to drinking‐water supply pipes
(2023) Nissler, Elisabeth; Scherrer, Samuel; Class, Holger; Müller, Tanja; Hermannspan, Mark; Osmancevic, Esad; Haslauer, Claus
Drinking‐water quality in supply pipe networks can be negatively affected by high temperatures during hot summer months due to detrimental bacteria encountering ideal conditions for growth. Thus, water suppliers are interested in estimating the temperature in their distribution networks. We investigate both experimentally and by numerical simulation the heat and water transport from ground surface into the subsurface, (i.e., above drinking‐water pipes). We consider the meteorological forcing functions by a sophisticated approach to model the boundary conditions for the heat balance at the soil-atmosphere interface. From August to December 2020, soil temperatures and soil moisture were measured dependent on soil type, land‐use cover, and weather data at a pilot site, constructed specifically for this purpose at the University of Stuttgart with polyethylene and cast‐iron pipes installed under typical in situ conditions. We included this interface condition at the atmosphere-subsurface boundary into an integrated non‐isothermal, variably saturated (Richards') the numerical simulator DuMux 3. This allowed, after calibration, to match measured soil temperatures with ±2°C accuracy. The land‐use cover influenced the soil temperature in 1.5 m more than the soil material used for back‐filling the trench above the pipe.
Open Access
Investigation of crystal growth in enzymatically induced calcite precipitation by micro-fluidic experimental methods and comparison with mathematical modeling
(2021) Wolff, Lars von; Weinhardt, Felix; Class, Holger; Hommel, Johannes; Rohde, Christian
Enzymatically induced calcite precipitation (EICP) is an engineering technology that allows for targeted reduction of porosity in a porous medium by precipitation of calcium carbonates. This might be employed for reducing permeability in order to seal flow paths or for soil stabilization. This study investigates the growth of calcium-carbonate crystals in a micro-fluidic EICP setup and relies on experimental results of precipitation observed over time and under flow-through conditions in a setup of four pore bodies connected by pore throats. A phase-field approach to model the growth of crystal aggregates is presented, and the corresponding simulation results are compared to the available experimental observations. We discuss the model’s capability to reproduce the direction and volume of crystal growth. The mechanisms that dominate crystal growth are complex depending on the local flow field as well as on concentrations of solutes. We have good agreement between experimental data and model results. In particular, we observe that crystal aggregates prefer to grow in upstream flow direction and toward the center of the flow channels, where the volume growth rate is also higher due to better supply.
Open Access
Machine learning assists in increasing the time resolution of X-ray computed tomography applied to mineral precipitation in porous media
(2023) Lee, Dongwon; Weinhardt, Felix; Hommel, Johannes; Piotrowski, Joseph; Class, Holger; Steeb, Holger
Many subsurface engineering technologies or natural processes cause porous medium properties, such as porosity or permeability, to evolve in time. Studying and understanding such processes on the pore scale is strongly aided by visualizing the details of geometric and morphological changes in the pores. For realistic 3D porous media, X-Ray Computed Tomography (XRCT) is the method of choice for visualization. However, the necessary high spatial resolution requires either access to limited high-energy synchrotron facilities or data acquisition times which are considerably longer (e.g. hours) than the time scales of the processes causing the pore geometry change (e.g. minutes). Thus, so far, conventional benchtop XRCT technologies are often too slow to allow for studying dynamic processes. Interrupting experiments for performing XRCT scans is also in many instances no viable approach. We propose a novel workflow for investigating dynamic precipitation processes in porous media systems in 3D using a conventional XRCT technology. Our workflow is based on limiting the data acquisition time by reducing the number of projections and enhancing the lower-quality reconstructed images using machine-learning algorithms trained on images reconstructed from high-quality initial- and final-stage scans. We apply the proposed workflow to induced carbonate precipitation within a porous-media sample of sintered glass-beads. So we were able to increase the temporal resolution sufficiently to study the temporal evolution of the precipitate accumulation using an available benchtop XRCT device.
Open Access
Models for non-isothermal compositional gas-liquid flow and transport in porous media
(2007) Class, Holger; Helmig, Rainer (Prof.)
Multiphase flow processes in porous media occur in many different fields of applications. One may basically distinguish between natural and technical porous media. A classical porous medium is the natural subsurface while there is still a number of technical porous media where flow and transport plays an important role and for which some basic model concepts developed for subsurface problems can be applied or at least adapted. One such technical porous medium is, for example, the gas diffusion layer of a fuel cell where the porous layer has the purpose of controlling the gas transport from the gas discharge channel to the reaction layer and concurrently the displacement of liquid water that is produced by the reaction. Major subsurface applications treated in this work are contaminant spreading in the saturated and unsaturated zone, thermally enhanced in-situ remediation methods, and the large topic of carbon dioxide storage in deep geologic formations. The latter got recently much attention in the discussions how to mitigate greenhouse gas concentrations and global warming. This work deals in particular with the numerical modeling of gas-liquid flow in porous media, thereby considering non-isothermal and compositional effects. The basic characteristics of the processes and different applications are explained and discussed. The fundamental concepts for the physical and mathematical models are introduced including their specific adaption to certain problems and a brief discussion of numerical solution algorithms. A large chapter presents example applications that illustrate the basic processes and phenomena by simulation results.
Open Access
A new simulation framework for soil-root interaction, evaporation, root growth, and solute transport
(2018) Koch, Timo; Heck, Katharina; Schröder, Natalie; Class, Holger; Helmig, Rainer
We have developed a general model concept and a flexible software framework for the description of plant-scale soil-root interaction processes including the essential fluid mechanical processes in the vadose zone. The model was developed in the framework of non-isothermal, multiphase, multicomponent flow and transport in porous media. The software is an extension of the open-source porous media flow and transport simulator DuMux to embedded mixed-dimensional coupled schemes. Our coupling concept allows us to describe all processes in a strongly coupled form and adapt the complexity of the governing equations in favor of either accuracy or computational efficiency. We have developed the necessary numerical tools to solve the strongly coupled nonlinear partial differential equation systems that arise with a locally mass conservative numerical scheme even in the context of evolving root architectures. We demonstrate the model concept and its features, discussing a virtual hydraulic lift experiment including evaporation, root tracer uptake on a locally refined grid, the simultaneous simulation of root growth and root water uptake, and an irrigation scenario comparing different models for flow in unsaturated soil. We have analyzed the impact of evaporation from soil on the soil water distribution around a single plant’s root system. Moreover, we have shown that locally refined grids around the root system increase computational efficiency while maintaining accuracy. Finally, we demonstrate that the assumptions behind the Richards equation may be violated under certain conditions.
Open Access
A numerical model for enzymatically induced calcium carbonate precipitation
(2020) Hommel, Johannes; Akyel, Arda; Frieling, Zachary; Phillips, Adrienne J.; Gerlach, Robin; Cunningham, Alfred B.; Class, Holger
Enzymatically induced calcium carbonate precipitation (EICP) is an emerging engineered mineralization method similar to others such as microbially induced calcium carbonate precipitation (MICP). EICP is advantageous compared to MICP as the enzyme is still active at conditions where microbes, e.g., Sporosarcina pasteurii, commonly used for MICP, cannot grow. Especially, EICP expands the applicability of ureolysis-induced calcium carbonate mineral precipitation to higher temperatures, enabling its use in leakage mitigation deeper in the subsurface than previously thought to be possible with MICP. A new conceptual and numerical model for EICP is presented. The model was calibrated and validated using quasi-1D column experiments designed to provide the necessary data for model calibration and can now be used to assess the potential of EICP applications for leakage mitigation and other subsurface modifications.
Open Access
Permeability estimation of regular porous structures : a benchmark for comparison of methods
(2021) Wagner, Arndt; Eggenweiler, Elissa; Weinhardt, Felix; Trivedi, Zubin; Krach, David; Lohrmann, Christoph; Jain, Kartik; Karadimitriou, Nikolaos; Bringedal, Carina; Voland, Paul; Holm, Christian; Class, Holger; Steeb, Holger; Rybak, Iryna
The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.
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, Holger
Microbially 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.
Open Access
Seasonal dynamics of gaseous CO2 concentrations in a karst cave correspond with aqueous concentrations in a stagnant water column
(2023) Class, Holger; Keim, Leon; Schirmer, Larissa; Strauch, Bettina; Wendel, Kai; Zimmer, Martin
Dissolved CO2 in karst water is the key driving force of karstification. Replenishment of CO2 concentrations in karst water occurs by meteoric water that percolates through the vadose zone, where CO2 produced from microbial activity is dissolved. CO2 can thus be transported with the percolating water or in the gas phase due to ventilation in karst systems. We measured seasonally fluctuating CO2 concentrations in the air of a karst cave and their influence on aqueous CO2 concentrations in different depths of a stagnant water column. The observed data were compared to numerical simulations. The data give evidence that density-driven enhanced dissolution of gaseous CO2 at the karst water table is the driving force for a fast increase of aqueous CO2 during periods of high gaseous concentrations in the cave, whereas during periods of lower gaseous concentrations, the decline of aqueous CO2 is limited to shallow water depths in the order of 1 m. This is significant because density-driven CO2 dissolution has not been previously considered relevant for karst hydrology in the literature. Attempts at reproducing the measured aqueous CO2 concentrations with numerical modeling revealed challenges related to computational demands, discretization, and the high sensitivity of the processes to tiny density gradients.
Open Access
Spatiotemporal distribution of precipitates and mineral phase transition during biomineralization affect porosity-permeability relationships
(2022) Weinhardt, Felix; Deng, Jingxuan; Hommel, Johannes; Vahid Dastjerdi, Samaneh; Gerlach, Robin; Steeb, Holger; Class, Holger
Enzymatically induced calcium carbonate precipitation is a promising geotechnique with the potential, for example, to seal leakage pathways in the subsurface or to stabilize soils. Precipitation of calcium carbonate in a porous medium reduces the porosity and, consequently, the permeability. With pseudo-2D microfluidic experiments, including pressure monitoring and, for visualization, optical microscopy and X-ray computed tomography, pore-space alterations were reliably related to corresponding hydraulic responses. The study comprises six experiments with two different pore structures, a simple, quasi-1D structure, and a 2D structure. Using a continuous injection strategy with either constant or step-wise reduced flow rates, we identified key mechanisms that significantly influence the relationship between porosity and permeability. In the quasi-1D structure, the location of precipitates is more relevant to the hydraulic response (pressure gradients) than the overall porosity change. In the quasi-2D structure, this is different, because flow can bypass locally clogged regions, thus leading to steadier porosity-permeability relationships. Moreover, in quasi-2D systems, during continuous injection, preferential flow paths can evolve and remain open. Classical porosity-permeability power-law relationships with constant exponents cannot adequately describe this phenomenon. We furthermore observed coexistence and transformation of different polymorphs of calcium carbonate, namely amorphous calcium carbonate, vaterite, and calcite and discuss their influence on the observed development of preferential flow paths. This has so far not been accounted for in the state-of-the-art approaches for porosity–permeability relationships during calcium carbonate precipitation in porous media.
Open Access
A study on Darcy versus Forchheimer models for flow through heterogeneous landfills including macropores
(2022) Winter, Roman; Valsamidou, Archontoula; Class, Holger; Flemisch, Bernd
Flow through heterogeneous landfills that include macropores may occur under Reynolds numbers higher than those where Darcy’s law is valid. Extensions, such as a Forchheimer approach, may be required to include inertial effects. Our aim is developing predictive models for such landfills that are built from the low-level radioactive waste and debris of dismantled nuclear power plants. It consists of different materials, which after crushing result in a spatially heterogeneous distribution of porous-media properties in the landfills. Rain events or leakage, for example, may wash out radionuclides and transport them with the water flow. We investigate here the water flow and consider an inclusion of macropores. To deal with possibly high velocities, we choose the Forchheimer model and, taking different Forchheimer coefficients into account, compare it to the Darcy model. The focal points of the study are (i) the influence of the macropores on the flow field and (ii) the impact of the choice of the Forchheimer coefficient both on the solution and the computational effort. The results show that dependent on their size, macropores can dominate the flow field. Furthermore, Forchheimer coefficients introducing more inertial effects are associated with considerably higher runtimes.
Open Access
Theorie und numerische Modellierung nichtisothermer Mehrphasenprozesse in NAPL-kontaminierten porösen Medien
(2001) Class, Holger; Helmig, Rainer (Prof. Dr.)
In dieser Arbeit werden die physikalischen Fragestellungen als auch die mathematisch-numerische Modellbildung der nichtisothermen Mehrphasen- und Mehrkomponentenprozesse in porösen Medien aufbereitet.
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, Holger
Calcium 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.