Philipp Schädle

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Schädle

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Philipp

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0000-0002-5485-2028

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Publications 1 - 8 of 8

Impact of Effective Normal Stress on Capillary Pressure in a Single Natural Fracture
Grimm Lima, Marina; Schädle, Philipp; Vogler, Daniel; et al. (2019)
Proceedings of the European Geothermal Congress 2019
Verification benchmarks for single-phase flow in three-dimensional fractured porous media
Berre, Inga; Schädle, Philipp; et al. (2021)
Advances in Water Resources
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, four benchmark cases for single-phase flow in three-dimensional fractured porous media are presented. 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.
Flow and transport through fractured rock - numerical approaches to account for fracture heterogeneity
Schädle, Philipp (2020)
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.
Comparison and application of non-conforming mesh models for flow in fractured porous media using dual Lagrange multipliers
Zulian, Patrick; Schädle, Philipp; Karagyaur, Liudmila; et al. (2022)
Journal of Computational Physics
Geological settings, such as reservoirs, include fractures with different material properties and geometric features. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow us to integrate various fracture geometries in a porous medium matrix. This study focuses on a modeling approach for single-phase flow in fractured porous media and its application to different types of non-conforming mesh models. We propose a combination of the Lagrange multiplier method with variational transfer techniques for simulating flow through fractured porous media by employing complex non-conforming geometries as well as hybrid- and equi-dimensional models and discretizations. The variational transfer is based on the L2-projection and enables an accurate and highly efficient parallel projection of fields between non-conforming meshes (e.g., between fracture and porous matrix domain). We present the different techniques as a unified mathematical framework with a practical perspective. By means of numerical examples we discuss both, performance and applicability of the particular strategies. Comparisons of finite element simulation results to widely adopted 2D benchmark cases show good agreement and the dual Lagrange multiplier spaces show good performance. In an extension to 3D fracture network, we first provide complementary results to a recently developed benchmark case and afterwards we explore a complex scenario which leverages the different types of fracture meshes. Complex and highly conductive fracture networks are found more suitable in combination with embedded hybrid-dimensional fractures. However, thick and blocking fractures are better approximated by equi-dimensional embedded fractures and the equi-dimensional mortar method, respectively.
A Lagrange multiplier method for single-phase flow in 3D discrete fractured porous media
Schädle, Philipp; Zulian, Patrick; Vogler, Daniel; et al. (2019)
Book of Abstracts of International Conference on Porous Media ~ Book of Abstracts InterPore2019 Valencia
Permeability Impairment and Salt Precipitation Patterns During CO2 Injection Into Single Natural Brine‐Filled Fractures
Grimm Lima, Marina; Schädle, Philipp; Green, Christopher P.; et al. (2020)
Water Resources Research
© 2020. American Geophysical Union. All Rights Reserved. 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-D 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.
A Numerical Model for Formation Dry-out During CO2 Injection in Fractured Reservoirs Using the MOOSE Framework: Implications for CO2-based Geothermal Energy Extraction
Grimm Lima, Marina Maria; Schädle, Philipp; Vogler, Daniel; et al. (2020)
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.
Numerical investigations of thermal attenuation and lag time in rough fractures: comparison of joint solute and heat tracer tests
Schädle, Philipp; Saar, Martin O.; Ebigbo, Anozie (2020)
Abstract Volume 18th Swiss Geoscience Meeting

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