REFEREED PUBLICATIONS IN JOURNALS
Berre, I., W. M. Boon, B. Flemisch, A. Fumagalli, D. Gläser, E. Keilegavlen, A. Scotti, I. Stefansson, et al., P. Schädle, and et al., Verification benchmarks for single-phase flow in three-dimensional fractured porous media, Advances in Water Resources, 147, pp. 103759, 2021. [Download PDF] [View Abstract]Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases.
Lima, M., P. Schädle, C. Green, D. Vogler, M.O. Saar, and X.-Z. Kong, Permeability Impairment and Salt Precipitation Patterns during CO2 Injection into Single Natural Brine-filled Fractures, Water Resources Research, 56/8, pp. e2020WR027213, 2020. [Download PDF] [View Abstract]Formation dry-out in fracture-dominated geological reservoirs may alter the fracture space, impair rock absolute permeability and cause a significant decrease in well injectivity. In this study, we numerically model the dry-out processes occurring during supercritical CO2 (scCO2) injection into single brine-filled fractures and evaluate the potential for salt precipitation under increasing effective normal stresses in the evaporative regime. We use an open-source, parallel finite-element framework to numerically model two-phase flow through 2-Dimensional fracture planes with aperture fields taken from naturally fractured granite cores at the Grimsel Test Site in Switzerland. Our results reveal a displacement front and a subsequent dry-out front in all simulated scenarios, where higher effective stresses caused more flow channeling, higher rates of water evaporation and larger volumes of salt precipitates. However, despite the larger salt volumes, the permeability impairment was lower at higher effective normal stresses. We conclude that the spatial distribution of the salt, precipitated in fractures with heterogeneous aperture fields, strongly affects the absolute permeability impairment caused by formation dry-out. The numerical simulations assist in understanding the behavior of the injectivity in fractures and fracture networks during subsurface applications that involve scCO2 injection into brine.
Schädle, P., P. Zulian, D. Vogler, S. Bhopalam R., M.G.C. Nestola, A. Ebigbo, R. Krause, and M.O. Saar, 3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers, Computers & Geosciences, 132, pp. 42-55, 2019. [Download PDF] [View Abstract]This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the applied finite element Lagrange multiplier spaces show good performance. The method is further evaluated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the variational transfer approach, is capable of modeling single-phase flow through realistic 3D fracture networks.
Schaedle, P., T. Kaempfer, G. Pepin, J. Wendling, and J. Bommundt, Combining high-resolution two-phase with simplified single-phase simulations in order to optimize the performance of PA/SA simulations for a deep geological repository for radioactive waste, Geological Society, London, Special Publications, 433/443/SP443.4, 2017. [Download PDF] [View Abstract]The transport of a radioactive solute during the transient thermo-hydraulic regime with gas generation in and around a disposal cell depends on complex multi-phase processes. Numerical simulations can improve the understanding of the system by providing detailed information on the temporal and spatial distribution of the radionuclides. In particular, their fluxes can be computed under the given transient conditions considering radionuclide, heat and gas release from the waste. However, such detailed multi-phase simulations are very demanding with respect to com- putational resources and time. Based on the knowledge gained from such complex simulations, we have developed a robust simplified single-phase approach for performance and safety assessment, the improved efficiency of which enables extensive parameter studies. The simplified approach comprises, on the one hand, homogenization of features of high detail and, on the other hand, the employment of two-phase simulation results that are used to deduce equivalent single-phase parameterizations. The results have been validated with various benchmark criteria at well-defined interfaces in the modelled disposal cells based on the simulated radionuclides fluxes.
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Lima, M., P. Schädle, D. Vogler, M. Saar, and X.-Z. Kong, A Numerical Model for Formation Dry-out During CO2 Injection in Fractured Reservoirs Using the MOOSE Framework: Implications for CO2-based Geothermal Energy Extraction, Proceedings of the World Geothermal Congress 2020, Reykjavík, Iceland, (in press). [View Abstract]Injection of supercritical carbon dioxide (scCO2) into geological reservoirs is involved in Carbon Capture, Utilization, and Storage (CCUS), such as geological CO2 storage, and Enhanced Geothermal Systems (EGS). The potential physico-chemical interactions between the dry scCO2, the reservoir fluid, and rocks may cause formation dry-out, where mineral precipitates due to continuous evaporation of water into the scCO2 stream. This salt precipitation may impair the rock bulk permeability and cause a significant decrease in the well injectivity. Formation dry-out and the associated salt precipitation during scCO2 injection into porous media have been investigated in previous studies by means of numerical simulations and laboratory experiments. However, few studies have focused on the dry-out effects in fractured rocks in particular, where the mass transport is strongly influenced by the fracture aperture distribution. In this study, we numerically model the dry-out processes occurring during scCO2 injection into brine-saturated single fractures and evaluate the potential of salt precipitation. Fracture aperture fields are photogrammetrically determined with fracture geometries of naturally fractured granite cores from the Deep Underground Geothermal (DUG) Lab at the Grimsel Test Site (GTS), in Switzerland. We use an open-source, parallel finite element framework to numerically model two-phase flow through a 2D fracture plane. Under in-situ reservoir conditions, the brine is displaced by dry scCO2 and also evaporates into the CO2 stream. The fracture permeability is calculated with the local cubic law. Additionally, we extend the numerical model by the Young-Laplace equation to determine the aperture-based capillary pressure. Finally, as future work, the precipitation of salt will be modelled by employing a uniform mineral growth approach, where the local aperture uniformly decreases with the increase in precipitated mineral volume. The numerical simulations assist in understanding the long-term behaviour of reservoir injectivity during subsurface applications that involve scCO2 injection, including CO2-based geothermal energy extraction.
Lima, M.M., P. Schädle, D. Vogler, M.O. Saar, and X.-Z. Kong, Impact of Effective Normal Stress on Capillary Pressure in a Single Natural Fracture, European Geothermal Congress 2019, pp. 1-9, 2019. [View Abstract]Multiphase fluid flow through rock fractures occurs in many reservoir applications such as geological CO2 storage, Enhanced Geothermal Systems (EGS), nuclear waste disposal, and oil and gas production. However, constitutional relations of capillary pressure versus fluid saturation, particularly considering the change of fracture aperture distributions under various stress conditions, are poorly understood. In this study, we use fracture geometries of naturally-fractured granodiorite cores as input for numerical simulations of two-phase brine displacement by super critical CO 2 under various effective normal stress conditions. The aperture fields are first mapped via photogrammetry, and the effective normal stresses are applied by means of a Fast Fourier Transform (FFT)-based convolution numerical method. Throughout the simulations, the capillary pressure is evaluated from the local aperture. Two approaches to obtain the capillary pressure are used for comparison: either directly using the Young-Laplace equation, or the van Genuchten equation fitted from capillary pressure-saturation relations generated using the pore-occupancy model. Analyses of the resulting CO2 injection patterns and the breakthrough times enable investigation of the relationships between the effective normal stress, flow channelling and aperture-based capillary pressures. The obtained results assist the evaluation of two-phase flow through fractures in the context of various subsurface applications.
Garapati, N., B.M. Adams, J.M. Bielicki, P. Schaedle, J.B. Randolph, T.H. Kuehn, and M.O. Saar, A Hybrid Geothermal Energy Conversion Technology - A Potential Solution for Production of Electricity from Shallow Geothermal Resources, Energy Procedia, 114, pp. 7107-7117, 2017. [Download PDF] [View Abstract]Geothermal energy has been successfully employed in Switzerland for more than a century for direct use but presently there is no electricity being produced from geothermal sources. After the nuclear power plant catastrophe in Fukushima, Japan, the Swiss Federal Assembly decided to gradually phase out the Swiss nuclear energy program. Deep geothermal energy is a potential resource for clean and nearly CO2-free electricity production that can supplant nuclear power in Switzerland and worldwide. Deep geothermal resources often require enhancement of the permeability of hot-dry rock at significant depths (4-6 km), which can induce seismicity. The geothermal power projects in the Cities of Basel and St. Gallen, Switzerland, were suspended due to earthquakes that occurred during hydraulic stimulation and drilling, respectively. Here we present an alternative unconventional geothermal energy utilization approach that uses shallower, lower-temperature, naturally permeable regions, that drastically reduce drilling costs and induced seismicity. This approach uses geothermal heat to supplement a secondary energy source. Thus this hybrid approach may enable utilization of geothermal energy in many regions in Switzerland and elsewhere, that otherwise could not be used for geothermal electricity generation. In this work, we determine the net power output, energy conversion efficiencies, and economics of these hybrid power plants, where the geothermal power plant is actually a CO2-based plant. Parameters varied include geothermal reservoir depth (2.5-4.5 km) and turbine inlet temperature (100-220 °C) after auxiliary heating. We find that hybrid power plants outperform two individual, i.e., stand-alone geothermal and waste-heat power plants, where moderate geothermal energy is available. Furthermore, such hybrid power plants are more economical than separate power plants.
Schädle, P., N. Hubschwerlen, and H. Class, Optimizing the Modeling Performance for Safety Assessments of Nuclear Waste Repositories by Approximating Two- Phase Flow and Transport by Single-Phase Transport Simulations”, Proceedings of the TOUGH Symposium 2012, 2012.
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Schädle, P., Flow and transport through fractured rock - Numerical approaches to account for fracture heterogeneity, Dissertation, ETH, 170 pp., 2020. [Download PDF] [View Abstract]Fractures and networks of fractures are relevant for a large number of subsurface engineering applications, such as geothermal energy utilization, drinking water supply, CO2 storage, and others. Fluid flow velocities in fractures often differ to those in the surrounding porous matrix by orders of magnitude and consequently, fractures largely govern the overall flow and transport characteristics of fractured reservoirs. Thereby, fractures can act as flow conduits, barriers, or a mixture of both. Moreover, due to the complex geometry of fractures and fracture networks, their impact on hydraulic properties can be very heterogeneous. To further complicate this issue the hydraulic properties are difficult to obtain from field experiments and subject to large uncertainties. Nonetheless, due to the relevance of fractures across subsurface applications, a detailed characterization of hydraulic properties is essential. Here, two possible approaches to improve the characterization of hydraulic properties are presented and discussed. First, the focus is on advancing our understanding of solute and heat tracer tests in single rough fractures. Secondly, an efficient numerical method to model flow through fractured porous media is presented. Hydraulic properties are commonly obtained by tracer tests in the field. A large number of artificial and natural solutes are used as tracers and heat as a tracer has increasingly been used in recent years. Due to the strong thermal interaction between the fracture fluid and the rock matrix heat tracer transport greatly differs from solute tracer transport. These differences show a characteristic behavior for simplified geometries, such as parallel plate with linear flow field, parallel plate with flow between two boreholes, and linear flow through channel(s). However, it remains unclear how these characteristic differences are affected by heterogeneous hydraulic properties of rough fractures. By numerical simulations of joint solute and heat tracer tests in a single rough fracture, we show that heat exchange in fractures with spatially variable apertures is closer to the parallel plate conceptual model than the channel(s) model. In summary, the relation of solute and heat tracer recovery varies strongly for fractures with variable apertures. The second part of this manuscript presents an efficient numerical method to model flow though fractured porous media. In such models fluid flow velocities and spatial scales range over several orders of magnitudes. Therefore, it is important that fractures are explicitly represented by discrete model domains, which results in discrete-fracture-matrix (DFM) models. Due to strong geometrical heterogeneities and uncertainties in fracture networks, efficient numerical models are necessary to perform stochastic studies with a large number of realizations. One of the limiting factors for such stochastic studies is the difficult and time consuming mesh generation for DFMs. To overcome this issue, non-conforming mesh methods have been developed over the past decades. One of these methods uses Lagrange multipliers and variational transfer for pressure coupling with non-conforming fracture and matrix meshes. By combining Lagrange multipliers with a 3D L2-projection variational transfer operator (LM–L2), we show the applicability of this method for large 3D DFMs. The method is validated with 2D benchmark cases and compared to reference results of complex 3D cases. The utilized space of dual Lagrange multipliers allows to reduce conditioning compared to other non-conforming methods. Taken together, the LM–L2 method is able to accurately compute pressure fields for large DFMs in 3D. Due to the complexity of 3D DFMs it is important to compare different numerical methods with each other. Therefore, we participated with the LM–L2 method in a large benchmark study where 17 different methods are compared. In this benchmark study flow through 3D fractured porous media was investigated. Additionally, advective transport is computed to facilitate comparison of the flow fields. So far, the LM–L2 method was employed to compute pressure fields. As such, it was necessary to extend the LM–L2 formulation for advective transport. The flow and transport results of the LM–L2 method are compared to all other methods for four benchmark cases, which test the general performance of the methods and their ability to represent challenging geometries and a large DFM. The results show that, due to the non-conforming meshes the LM–L2 method is advantageous for complex fracture geometries and the 3D variational transfer operator handles challenging setups naturally. The pressure fields for all benchmark cases show good agreement with the other methods. However, the concentration results are less accurate, which is due to the very coarse meshes and additional challenges such as numerical diffusion and mass conservation. Improvements could be made with local adaptive mesh refinement. In summary, the presented work improves our understanding of flow and transport processes in the context of subsurface fracture applications in two ways. To be more precise, the focus is on the impact of fracture heterogeneity in tracer tests and 3D DFMs. First, heat transfer characteristics in rough fractures are described in detail and information to refine the relationship between solute and heat tracers is given. This contributes to a better characterization of hydraulic properties of fractured systems. Additionally, a numerical, non-conforming mesh method for flow was examined and applied for challenging and complex networks of fractured porous media. The advantage of this method lies in the convenient mesh generation of geometrically complex fracture networks and its applicability for stochastic studies.
Schaedle, P., Rechenzeitoptimierung bei numerischen Sicherheitsabschätzungen für Atommüll-Endlager, MSc Thesis, University of Stuttgart, 82 pp., 2012. [View Abstract]Seit Mitte der 50er Jahre werden Atomkraftwerke gebaut und somit auch Abfälle produziert, die grosse Schwierigkeiten in der Handhabung und Lagerung mit sich bringen. Das grösste Problem liegt nicht in der Menge der Abfälle, sondern in der langanhaltenden schädlichen Strahlendosis die von den Abfällen abgegeben wird. Die momentan wissenschaftlich und wirtschaftlich vorherrschende Meinung ist, den Müll in geologischen Tiefenlagern zu deponieren. In der Vergangenheit wurden bereits unterschiedliche Gesteinsformationen als Endlagerstätten untersucht, getestet und auch eingesetzt. Viele haben sich jedoch als ungeeignet für die Deponierung atomaren Abfalls herausgestellt. Derzeit werden in Frankreich und der Schweiz Tonformationen als potenzielle Endlagerstandorte untersucht. Die geringe Durchlässigkeit und gleichermassen die über einen langen Zeitraum anhaltende Verschlusswirkung in Bezug auf Druck und Temperatur zeichnen eine Tonformation gegenüber Salz- oder Kristallinformationen aus. Zur Beurteilung eines potenziellen Endlagerstandorts werden geologische Erkundungen und Studien durchgeführt. Nach der ersten Erkundungsphase gilt es den Standort genauer zu untersuchen und das Gestein hinsichtlich seines Verhaltens während der Einlagerung zu verstehen. Um letztendlich eine Aussage über die Leistungsfähigkeit und Sicherheit eines potenziellen Endlagers machen zu können, sind auf Grundlage der zuvor gewonnenen Erkenntnisse umfangreiche numerische Simulationen nötig. Im Rahmen dieser Simulationen müssen unter anderem in der näheren Umgebung der Einlagerungsstollen hochaufgelöste Detailmodelle erstellt werden. Diese Modelle stellen die komplexen physikalischen Prozesse dar, die während der Einlagerung und nach dem Verschluss des Stollens ablaufen. Um möglichst viele Erkenntnisse über eventuelle Ereignisse oder Parameterunsicherheiten zu sammeln, müssen zusätzlich zu diesen Detailmodellen, deterministische und probabilistische Sicherheitsanalysen durchgeführt werden. Diese Arbeit wird bei der AF-Consult Switzerland AG im Rahmen eines durch die französische ANDRA (Agence nationale pour la gestion des déchets radioactifs – Französische nationale Agentur für die Entsorgung radioaktiver Abfälle) beauftragten Projekts durchgeführt. Dieses befasst sich mit der Optimierung und der effektiveren Umsetzung der Simulationen zur Berechnung der Radionuklidausbreitung. Durch die Projektvorgaben der ANDRA wird sich diese Arbeit an dem Endlagerkonzept der ANDRA orientieren. Die erarbeiteten numerischen Methoden sind aber gleichermassen auf andere Konzepte und Aufgabenstellungen anwendbar. Ein im Zusammenhang mit dieser Arbeit verfasster Konferenzbeitrag für das „TOUGH Symposium 2012“ wurde mit dem „Karsten Pruess Student Paper Award“ ausgezeichnet.