G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

RHEA v1.0: Enabling fully coupled simulations with hydro-geomechanical heterogeneity

Realistic modelling of tightly coupled hydro-geomechanical processes is relevant for the assessment of many hydrological and geotechnical applications. Such processes occur in geologic formations and are influenced by natural heterogeneity. Current numerical libraries offer capabilities and physics couplings that have proven to be valuable in many geotechnical fields like gas storage, rock fracturing and Earth resources extraction. However, implementation and verification of the full heterogeneity of subsurface properties using high-resolution field data in coupled simulations has not been done before. We develop, verify and document RHEA (Real HEterogeneity App), an open-source, fully coupled, finite-element application capable of including element-resolution hydro-geomechanical properties in coupled simulations. To extend current modelling capabilities of the Multiphysics Object-Oriented Simulation Environment (MOOSE), we added new code that handles spatially distributed data of all hydro-geomechanical properties. We further propose a simple yet powerful workflow to facilitate the incorporation of such data to MOOSE. We then verify RHEA with analytical solutions in one and two dimensions and propose a benchmark semi-analytical problem to verify heterogeneous systems with sharp gradients. Finally, we demonstrate RHEA\u27s capabilities with a comprehensive example including realistic properties. With this we demonstrate that RHEA is a verified open-source application able to include complex geology to perform scalable, fully coupled, hydro-geomechanical simulations. Our work is a valuable tool to assess challenging real-world hydro-geomechanical systems that may include different levels of complexity like heterogeneous geology and sharp gradients produced by contrasting subsurface properties

Characterization of fractured porous media using multivariate statistics and hydraulic travel time tomography

Fractured hard rocks are important in engineering, geotechnical, and hydrogeological practice because they act as hydraulic conductors providing pathways for fluid flow or barriers that prevent flow across them. In this thesis fractured porous media such as sandstones, which show a significant permeability of the matrix, are treated. In comparison to low permeable hard rocks such as granite and gneiss, fractured porous media show significant storage, flow, and transport e.g. of contaminants within the matrix. This has to be taken into account by the evaluation of flow and transport experiments. A fundamental step in understanding and predicting the behavior of fractured porous aquifers involves the identification of the spatial distribution of hydraulically significant features. Therefore, high resolution flow and transport data sets are required. Two different approaches are applied in order to evaluate high resolution flow and transport experiments arranged in a tomographical array. First, a multivariate statistical approach for the analysis of meso-scale flow and transport experiments is proposed. Within the statistical approach flow and transport measurements are classified into quasihomogeneous groups in order to determine properties and parameter zonation, which control flow and transport. The methodology was applied to a data set of gas flow and tracer experiments conducted to a gas saturated, fissured sandstone block of 60 × 60 × 60 cm3 in size. The agreement of the classification results with a geological surface mapping and numerical simulations show that it is possible to characterize and simplify complex systems without losing essential information about the investigated system. In the second part a travel time based hydraulic tomographic approach is proposed. The approach provides the inversion of travel times of hydraulic or pneumatic tests conducted in a tomographic array. The inversion is based on the relation between the peak time of a recorded transient pressure curve and the diffusivity of the investigated system. The development of a transformation factor enables the inversion of further travel times besides the peak time of a transient curve. As the early travel times of the curve are mainly related to preferential flow features while the inversion based on late travel times reflect an integral behavior, it can be assumed that the different inversion results reflect the properties of the overall system. The method has been applied to data from a set of pneumatic short term tests conducted to a gas saturated fractured sandstone cylinder with a height of 34 cm and a diameter of 31 cm. The three-dimensional reconstructions of the diffusivity distribution are found to be highly reliable and robust. In particular, the mapped fracture of the sandstone cylinder coincides with the reconstructed diffusivity distribution. In order to get a better insight of the hydraulic travel time approach, synthetic data sets are used. The synthetic data sets comprise simulated slug tests conducted in a tomographical array. The main focus of the synthetic study is to appraise the influence of the various travel times on the inversion results in dependence of the permeability distribution of the investigated geological medium. The inversion results are showing a strong dependence on the used travel times. The comparison of the different reconstructions based on different travel times with the forward model allows the verification and appraisal of the quality of the inversion. Hence, it is possible to suggest which travel time is most suited to reconstruct a certain subsurface structure.Geklüftete Festgesteine sind wichtig im Rahmen der ingenieurtechnischen, geotechnischen und hydrogeologischen Praxis, da sie entweder als hydraulische Leiter agieren und somit bevorzugte Fließpfade für Fluide darstellen oder sie die Eigenschaften von Geringleiter aufweisen und somit hydraulische Barrieren darstellen. In dieser Arbeit werden geklüftet poröse Festgesteine untersucht, die eine signifikante Matrixpermeabilität aufweisen. Im Vergleich zu gering durchlässigen Festgesteinen wie Granit oder Gneis weisen geklüftet poröse Medien bedeutende Speicher-, Strömung- und Transportkapazitäten auf, was sich z.B. auf den Transport von Schadstoffen innerhalb der Matrix auswirkt. Dies muss bei der Auswertung von Strömungs- und Transportexperimenten berücksichtigt werden. Ein grundlegender Schritt zum Verständnis und zur Vorhersage des Verhaltens von geklüftet porösen Aquiferen ist die Identifizierung der räumlichen Verteilung hydraulisch signifikanter Merkmale. Dafür werden hochauflösende Strömungs- und Transportdatensätze benötigt. Zur Auswertung der hochauflösenden Strömungs- und Transportexperimente, die unter Verwendung einer tomographischen Messanordnung aufgezeichnet worden sind, werden zwei unterschiedliche Ansätze verfolgt. Zuerst wird ein multivariater statistischer Ansatz für die Analyse von Strömungs- und Transportexperimenten vorgestellt. In diesem statistischen Ansatz werden Strömungs- und Transportmessungen in quasi homogene Gruppen eingeteilt, um die Eigenschaften und Parameterzonierung, die Strömung und Transport kontrollieren, zu bestimmen. Mit dieser Methode sind Strömungs- und Transportexperimente ausgewertet worden, die an einem gasgesättigten, geklüfteten Sandsteinblock mit einer Kantenlänge von 60 cm durchgeführt wurden. Die Klassifikationsergebnisse stimmen mit der geologischen Oberflächenkartierung und den numerischen Simulationen überein. Dies zeigt, dass es mit Hilfe des verwendeten Ansatzes möglich ist, komplexe Systeme zu charakterisieren und zu vereinfachen, ohne dass wichtige Systeminformationen verloren gehen. Im zweiten Teil wird ein auf Laufzeiten basierender Ansatz zur hydraulischen Tomographie vorgestellt. Dieser Ansatz umfasst die Inversion von Laufzeiten hydraulischer oder pneumatischer Tests, die unter Verwendung einer tomographischen Messanordnung aufgezeichnet worden sind. Die Inversion beruht dabei auf dem Zusammenhang zwischen der Laufzeit der maximalen Signaländerung eines aufgezeichneten instationären Signals und der Diffusivität des untersuchten Systems. Die Entwicklung eines Transformationsfaktors ermöglicht die Inversion von weiteren Laufzeiten, neben der Laufzeit der maximalen Änderung eines instationären Signals. Da frühe Laufzeiten einer aufgezeichneten Druckkurve überwiegend bevorzugte Flieswege und spätere Laufzeiten das integrale Verhalten des untersuchten Systems widerspiegeln, kann davon ausgegangen werden, dass die unterschiedlichen Inversionsergebnis das Verhalten des Gesamtsystems repräsentieren. Mit diese Methode wurden Daten von pneumatischen Kurzzeittests ausgewertet. Diese Daten sind an einem gasgesättigten, geklüfteten Sandsteinzylinder mit einer Höhe von 34 cm und einem Durchmesser von 31 cm aufgezeichnet worden. Die Ergebnisse der dreidimensionalen Diffusivitätsrekonstruktionen haben sich als zuverlässig und stabil erwiesen. Insbesondere zeigt die dreidimensionale Rekonstruktion der Diffusivitätsverteilung eine hohe Übereinstimmung mit der Lage der Kluft innerhalb des Zylinders. Um neue Erkenntnisse auf dem Gebiet der hydraulische Laufzeittomographie zu gewinnen, sind synthetische Datensätze verwendet worden. Die synthetischen Datensätze umfassen Slug-Tests, die unter Verwendung einer tomographischen Messanordnung modelliert worden sind. Ziel der synthetischen Fallstudie ist, den Einfluss unterschiedlicher Laufzeiten auf das Inversionsergebnis, in Abhängigkeit von der Permeabilitätsverteilung des untersuchten geologischen Mediums, zu bewerten. Die Inversionsergebnisse zeigen eine deutliche Abhängigkeit von den verwendeten Laufzeiten. Durch einen Vergleich zwischen den Diffusivitätsrekonstruktionen, die auf unterschiedlichen Laufzeiten basieren, und dem verwendeten Vorwärtsmodell ist es möglich, die Qualität der Inversionsergebnisse zu bewerten und zu überprüfen. Somit kann eine Inversionsstrategie vorgeschlagen werden, die für den jeweiligen Untergrund am besten geeignet ist

Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2005-2006Un modèle numérique tridimensionnel a été développé pour la simulation du système chimique quartz-eau couplé avec l’écoulement à densité et viscosité variable dans les milieux poreux discrètement fracturés. Le nouveau modèle simule aussi le transfert de chaleur dans les milieux poreux fracturés en supposant que l’expansion thermique du milieu est négligeable. Les propriétés du fluide, densité et viscosité, ainsi que les constantes chimiques (constant de taux de dissolution, constant d’équilibre, coefficient d’activité) sont calculées en fonction de la concentration des ions majeurs et de la température. Des paramètres de réaction et d’écoulement, comme la surface spécifique du minéral et la perméabilité sont mis jour à la fin de chaque pas de temps avec des taux de réaction explicitement calculés. Le modèle suppose que des changements de la porosite et des ouvertures de fractures n’ont pas d’impact sur l’emmagasinement spécifique. Des pas de temps adaptatifs sont utilisés pour accélérer et ralentir la simulation afin d’empêcher des résultats non physiques. Les nouveaux incréments de temps dépendent des changements maximum de la porosité et/ou de l’ouverture de fracture. Des taux de réaction au niveau temporel L+1 (schéma de pondération temporelle implicite) sont utilisés pour renouveler tous les paramètres du modèle afin de garantir la stabilité numérique. Le modèle a été vérifié avec des problèmes analytiques, numériques et physiques de l’écoulement à densité variable, transport réactif et transfert de chaleur dans les milieux poreux fracturés. La complexité de la formulation du modèle permet d’étudier des réactions chimiques et l’écoulement à densité variable d’une façon plus réaliste qu’auparavant possible. En premier lieu, cette étude adresse le phénomène de l’écoulement et du transport à densité variable dans les milieux poreux fracturés avec une seule fracture à inclinaison arbitraire. Une formulation mathématique générale du terme de flottabilité est dérivée qui tient compte de l’écoulement et du transport à densité variable dans des fractures de toute orientation. Des simulations de l’écoulement et du transport à densité variable dans une seule fracture implanté dans une matrice poreuse ont été effectuées. Les simulations montrent que l’écoulement à densité variable dans une fracture cause la convection dans la matrice poreuse et que la fracture à perméabilité élevée agit comme barrière pour la convection. Le nouveau modèle a été appliqué afin de simuler des exemples, comme le mouvement horizontal d’un panache de fluide chaud dans un milieu fracturé chimiquement réactif. Le transport thermohalin (double-diffusif) influence non seulement l’écoulement à densité variable mais aussi les réactions chimiques. L’écoulement à convection libre dépend du contraste de densité entre le fluide (panache chaud ou de l’eau salée froide) et le fluide de référence. Dans l’exemple, des contrastes de densité sont généralement faibles et des fractures n’agissent pas comme des chemins préférés mais contribuent à la dispersion transverse du panache. Des zones chaudes correspondent aux régions de dissolution de quartz tandis que dans les zones froides, la silice mobile précipite. La concentration de silice est inversement proportionnelle à la salinité dans les régions à salinité élevée et directement proportionnelle à la température dans les régions à salinité faible. Le système est le plus sensible aux inexactitudes de température. Ceci est parce que la température influence non seulement la cinétique de dissolution (équation d’Arrhenius), mais aussi la solubilité de quartz.A three-dimensional numerical model is developed that couples the quartz-water chemical system with variable-density, variable-viscosity flow in fractured porous media. The new model also solves for heat transfer in fractured porous media, under the assumption of negligible thermal expansion of the rock. The fluid properties density and viscosity as well as chemistry constants (dissolution rate constant, equilibrium constant and activity coefficient) are calculated as a function of the concentrations of major ions and of temperature. Reaction and flow parameters, such as mineral surface area and permeability, are updated at the end of each time step with explicitly calculated reaction rates. The impact of porosity and aperture changes on specific storage is neglected. Adaptive time stepping is used to accelerate and slow down the simulation process in order to prevent physically unrealistic results. New time increments depend on maximum changes in matrix porosity and/or fracture aperture. Reaction rates at time level L+1 (implicit time weighting scheme) are used to renew all model parameters to ensure numerical stability. The model is verified against existing analytical, numerical and physical benchmark problems of variable-density flow, reactive solute transport and heat transfer in fractured porous media. The complexity of the model formulation allows chemical reactions and variable-density flow to be studied in a more realistic way than previously possible. The present study first addresses the phenomenon of variable-density flow and transport in fractured porous media, where a single fracture of an arbitrary incline can occur. A general mathematical formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulations of variable-density flow and solute transport are conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the highpermeability fracture acts as a barrier for convection. The new model was applied to simulate illustrative examples, such as the horizontal movement of a hot plume in a chemically reactive fractured medium. Thermohaline (double-diffusive) transport impacts both buoyancy-driven flow and chemical reactions. Free convective flow depends on the density contrast between the fluid (hot brine or cool saltwater) and the reference fluid. In the example, density contrasts are generally small and fractures do not act like preferential pathways but contribute to transverse dispersion of the plume. Hot zones correspond to areas of quartz dissolution while in cooler zones, precipitation of imported silica prevails. The silica concentration is inversely proportional to salinity in high-salinity regions and directly proportional to temperature in low-salinity regions. The system is the most sensitive to temperature inaccuracy. This is because temperature impacts both the dissolution kinetics (Arrhenius equation) and the quartz solubility

Geostatistical and Stochastic Study of Radio nuclide Transport in the Unsaturated Zone at Yucca Mountain

The U.S. Nuclear Waste Technical Review Board [Cohon et al. 1998] evaluated the technical and scientific validity of activities undertaken by the Secretary of Energy to characterize Yucca Mountain, Nevada, for its suitability as an underground repository in which to store high-level radioactive waste and spent nuclear fuel. In the report, the Board pinpointed that the study on groundwater flow and radionuclide transport in the saturated and unsaturated zones below Yucca Mountain should, over the next several years, focus on reducing prediction uncertainty. In its 2002, the Board repeated this concern by stating, “… hydrogeologic processes that affect radionuclide transport below the proposed repository in the unsaturated and saturated zones remain poorly understood.” However, above the saturated zone, the unsaturated zone (UZ), the area in which the repository would be located, acts as a critical natural barrier by delaying the arrival of radionuclides at the saturated zone and by reducing radionuclide concentrations in groundwater through dispersion and dilution. Before any analysis of saturated zone behavior becomes relevant, quantitative prediction of radionuclide transport in the unsaturated zone becomes critical for performance assessment and design of the repository of the Yucca Mountain Project (YMP)

Reactive transport model of gypsum karstification in physically and chemically heterogeneous fractured media

[Abstract:] Gypsum dissolution leads to the development of karstic features within much shorter timescales than in other sedimentary rocks, potentially leading to rapid deterioration of groundwater quality and increasing the risk of catastrophes caused by subsidence. Here, we present a 2-D reactive transport model to evaluate gypsum karstification in physically and chemically heterogeneous systems. The model considers a low-permeability rock matrix composed mainly of gypsum and a discontinuity (fracture), which acts as a preferential water pathway. Several scenarios are analyzed and simulated to investigate the relevance for gypsum karstification of: (1) the dynamic update of flow and transport parameters due to porosity changes; (2) the spatial distribution of minerals in the rock matrix; (3) the time evolution of water inflows through the boundaries of the model; (4) the functions relating permeability, k, to porosity, ϕ. The average porosity of the matrix after 1000 years of simulation increases from 0.045 to 0.29 when flow, transport, and chemical parameters and the water inflows through the boundary are dynamically updated according to the porosity changes. On the contrary, the porosity of the matrix hardly changes when the porosity feedback effect is not considered, while its average increases to 0.13 if the water inflow occurs through the discontinuity. Moreover, the dissolution of small amounts of highly soluble sulfate minerals plays a major role in the development of additional fractures. The increase in hydraulic conductivity is largest for the power law with an exponent of n = 5, as well as the Kozeny-Carman and the modified Fair-atch k-ϕ relationships. The gypsum dissolution front propagates into the matrix faster when the power law with n = 2 and 3 and the Verma–Pruess k-ϕ relationships are used.Ministerio de Economía y Competitividad; PID2019-109544RB-I00Xunta de Galicia; ED431C2021/5

Mini-Workshop: Numerical Upscaling for Flow Problems: Theory and Applications

The objective of this workshop was to bring together researchers working in multiscale simulations with emphasis on multigrid methods and multiscale finite element methods, aiming at chieving of better understanding and synergy between these methods. The goal of multiscale finite element methods, as upscaling methods, is to compute coarse scale solutions of the underlying equations as accurately as possible. On the other hand, multigrid methods attempt to solve fine-scale equations rapidly using a hierarchy of coarse spaces. Multigrid methods need “good” coarse scale spaces for their efficiency. The discussions of this workshop partly focused on approximation properties of coarse scale spaces and multigrid convergence. Some other presentations were on upscaling, domain decomposition methods and nonlinear multiscale methods. Some researchers discussed applications of these methods to reservoir simulations, as well as to simulations of filtration, insulating materials, and turbulence

Thermal Plume Transport From Sand and Gravel Pits Potential Thermal Impacts on Cool-Water Streams

Potential thermal impacts from below-water-table aggregate extraction on a cool-water stream were investigated by monitoring thermal plumes, moving through an unconfined glacial-outwash aquifer, and assessing their subsurface persistence. The growing demand for aggregate and increased pressure to pursue extraction in ecologically sensitive areas has driven the need for this work. During a 10-year period, ground and surface water temperatures were measured monthly, including two periods of intensive monitoring (22 months and 2.5 years). The aquifer hydraulic conductivity (K) is quantified at the laboratory and field scale. The mean K’s from the multi-scale tests depend on test-support volume and span two-orders of magnitude, 1.8×10–4 to 1.7×10–2 m s–1. The effective thermal conductivity λ is characterized at an unprecedented level of detail by: (i) measuring the thermal conductivity of the soil solids, ls using the steady-state divided-bar apparatus and estimating conductivity from mineral composition; (ii) measuring the volumetric water content and porosity using cross-hole ground-penetrating radar; (iii) evaluating four models used to predict the apparent thermal conductivity, l, of variably saturated soils (iv) calculating the l field on a 0.25-m square cell grid using measured data and the selected model, and (v) simulating thermal transport within the two-dimensional domain using a finite-element numerical model. The apparent thermal conductivity in the saturated aquifer ranges from 2.14 to 2.69 W m-1 K-1 with a mean of 2.42 W m-1 K-1. These measurement and model methods may be used at other sites to construct thermal conductivity distributions for similar glacial soils. The annual temperature amplitude in the pit is 10ºC greater than the up gradient groundwater, resulting in alternating warm and cool plumes that persist in the aquifer for 11-months and migrate up to 250 m down gradient. The observed plume velocity (1.2 m d–1) lags the groundwater velocity (2.8 m d–1) due to thermal retardation. Using field data a conceptual model is developed, and implemented in a three-dimensional finite-element numerical model. While this work focused on plume migration, these results demonstrate that assessing impacts on the aquatic community requires an integrated, multi-disciplinary study. This work can guide such assessments